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Thermodynamic integration from classical to quantum mechanics.
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable. PMID:22168684
Habershon, Scott; Manolopoulos, David E
Cell motility and thermodynamic fluctuations tailoring quantum mechanics for biology
Cell motility underlying muscle contraction is an instance of thermodynamics tailoring quantum mechanics for biology. Thermodynamics is intrinsically multi-agential in admitting energy consumers in the form of energy-deficient thermodynamic fluctuations. The onset of sliding movement of an actin filament on myosin molecules in the presence of ATP molecules to be hydrolyzed demonstrates that thermodynamic fluctuations transform their nature so as
Koichiro Matsuno
Black hole thermodynamics from near-horizon conformal quantum mechanics
The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with D{>=}4). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamics from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their 'coordinate singularity', can be used self-consistently to describe the thermodynamics of black holes.
Camblong, Horacio E. [Department of Physics, University of San Francisco, San Francisco, California 94117-1080 (United States); Ordonez, Carlos R. [Department of Physics, University of Houston, Houston, Texas 77204-5506 (United States); World Laboratory Center for Pan-American Collaboration in Science and Technology, University of Houston Center, Houston, Texas 77204-5506 (United States)
Thermodynamical contours of electronic-vibrational spectra simulated using the statistical quantum�mechanical methods
Three polycyclic organic molecules in various solvents focused on thermo-dynamical aspects were theoretically investigated\\u000a using the recently developed statistical quantum mechanical\\/classical molecular dynamics method for simulating electronic-vibrational\\u000a spectra. The absorption bands of estradiol, benzene, and cyanoanthracene have been simulated, and most notably, the increase\\u000a in the spectral intensity for the lowest excited state transition as the temperature is increased observed
Vladimir PomogaevAnna Pomogaeva; Anna Pomogaeva; Pavel Avramov; K. J. Jalkanen; Sergey Kachin
Quantum thermodynamic cycles and quantum heat engines. II.
NASA Astrophysics Data System (ADS)
We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.
Quan, H. T.
Quantum thermodynamic cycles and quantum heat engines. II.
We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine. PMID:19518195
Quan, H T
Quantum mechanics based force field for carbon (QMFF-Cx) validated to reproduce the mechanical and thermodynamics properties of graphite.
As assemblies of graphene sheets, carbon nanotubes, and fullerenes become components of new nanotechnologies, it is important to be able to predict the structures and properties of these systems. A problem has been that the level of quantum mechanics practical for such systems (density functional theory at the PBE level) cannot describe the London dispersion forces responsible for interaction of the graphene planes (thus graphite falls apart into graphene sheets). To provide a basis for describing these London interactions, we derive the quantum mechanics based force field for carbon (QMFF-Cx) by fitting to results from density functional theory calculations at the M06-2X level, which demonstrates accuracies for a broad class of molecules at short and medium range intermolecular distances. We carried out calculations on the dehydrogenated coronene (C24) dimer, emphasizing two geometries: parallel-displaced X (close to the observed structure in graphite crystal) and PD-Y (the lowest energy transition state for sliding graphene sheets with respect to each other). A third, eclipsed geometry is calculated to be much higher in energy. The QMFF-Cx force field leads to accurate predictions of available experimental mechanical and thermodynamics data of graphite (lattice vibrations, elastic constants, Poisson ratios, lattice modes, phonon dispersion curves, specific heat, and thermal expansion). This validates the use of M06-2X as a practical method for development of new first principles based generations of QMFF force fields. PMID:20942530
Pascal, Tod A; Karasawa, Naoki; Goddard, William A
Quantum mechanics based force field for carbon (QMFF-Cx) validated to reproduce the mechanical and thermodynamics properties of graphite
NASA Astrophysics Data System (ADS)
As assemblies of graphene sheets, carbon nanotubes, and fullerenes become components of new nanotechnologies, it is important to be able to predict the structures and properties of these systems. A problem has been that the level of quantum mechanics practical for such systems (density functional theory at the PBE level) cannot describe the London dispersion forces responsible for interaction of the graphene planes (thus graphite falls apart into graphene sheets). To provide a basis for describing these London interactions, we derive the quantum mechanics based force field for carbon (QMFF-Cx) by fitting to results from density functional theory calculations at the M06-2X level, which demonstrates accuracies for a broad class of molecules at short and medium range intermolecular distances. We carried out calculations on the dehydrogenated coronene (C24) dimer, emphasizing two geometries: parallel-displaced X (close to the observed structure in graphite crystal) and PD-Y (the lowest energy transition state for sliding graphene sheets with respect to each other). A third, eclipsed geometry is calculated to be much higher in energy. The QMFF-Cx force field leads to accurate predictions of available experimental mechanical and thermodynamics data of graphite (lattice vibrations, elastic constants, Poisson ratios, lattice modes, phonon dispersion curves, specific heat, and thermal expansion). This validates the use of M06-2X as a practical method for development of new first principles based generations of QMFF force fields.
Pascal, Tod A.; Karasawa, Naoki; Goddard, William A.
A hierarchical approach to accurate predictions of macroscopic thermodynamic behavior from quantum mechanics and molecular simulations
NASA Astrophysics Data System (ADS)
The combination of molecular simulations and potentials obtained from quantum chemistry is shown to be able to provide reasonably accurate thermodynamic property predictions. Gibbs ensemble Monte Carlo simulations are used to understand the effects of small perturbations to various regions of the model Lennard-Jones 12-6 potential. However, when the phase behavior and second virial coefficient are scaled by the critical properties calculated for each potential, the results obey a corresponding states relation suggesting a non-uniqueness problem for interaction potentials fit to experimental phase behavior. Several variations of a procedure collectively referred to as quantum mechanical Hybrid Methods for Interaction Energies (HM-IE) are developed and used to accurately estimate interaction energies from CCSD(T) calculations with a large basis set in a computationally efficient manner for the neon-neon, acetylene-acetylene, and nitrogen-benzene systems. Using these results and methods, an ab initio, pairwise-additive, site-site potential for acetylene is determined and then improved using results from molecular simulations using this initial potential. The initial simulation results also indicate that a limited range of energies important for accurate phase behavior predictions. Second virial coefficients calculated from the improved potential indicate that one set of experimental data in the literature is likely erroneous. This prescription is then applied to methanethiol. Difficulties in modeling the effects of the lone pair electrons suggest that charges on the lone pair sites negatively impact the ability of the intermolecular potential to describe certain orientations, but that the lone pair sites may be necessary to reasonably duplicate the interaction energies for several orientations. Two possible methods for incorporating the effects of three-body interactions into simulations within the pairwise-additivity formulation are also developed. A low density approximation for the pair and three-body distribution functions is simpler to implement, but the results based on the numerical solution of the inhomogeneous Ornstein-Zernike equation using the Percus-Yevick closure are more accurate. Given the low temperatures for phase equilibria of the model system, neon, several approximations to estimate the quantum effects on the atomic nuclei are presented with reasonable success.
Garrison, Stephen L.
Quantum thermodynamic cycles and quantum heat engines.
In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine. PMID:17930197
Quan, H T; Liu, Yu-xi; Sun, C P; Nori, Franco
Quantum mechanics based force field for carbon (QMFF-Cx) validated to reproduce the mechanical and thermodynamics properties of graphite
As assemblies of graphene sheets, carbon nanotubes, and fullerenes become components of new nanotechnologies, it is important to be able to predict the structures and properties of these systems. A problem has been that the level of quantum mechanics practical for such systems (density functional theory at the PBE level) cannot describe the London dispersion forces responsible for interaction of
Tod A. Pascal; Naoki Karasawa; William A. Goddard
NSDL National Science Digital Library
This website contains a number of descriptions of quantum mechanical phenomena, using 3D animations to illustrate the physics. The goal is to introduce basic concepts and phenomena using simulations rather than complex mathematics. The time-dependence of quantum systems is a focus of this material.
Michielsen, Kristel; De Raedt, Hans
Quantum dynamics in the thermodynamic limit
The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum-mechanical building blocks is one of the cornerstones of modern condensed-matter theory and has found applications in many different areas of physics. The theory of spontaneous symmetry breaking, however, is inherently an equilibrium theory, which does not address the dynamics of quantum systems in the thermodynamic limit. Here, we will use the example of a particular antiferromagnetic model system to show that the presence of a so-called thin spectrum of collective excitations with vanishing energy - one of the well-known characteristic properties shared by all symmetry-breaking objects - can allow these objects to also spontaneously break time-translation symmetry in the thermodynamic limit. As a result, that limit is found to be able, not only to reduce quantum-mechanical equilibrium averages to their classical counterparts, but also to turn individual-state quantum dynamics into classical physics. In the process, we find that the dynamical description of spontaneous symmetry breaking can also be used to shed some light on the possible origins of Born's rule. We conclude by describing an experiment on a condensate of exciton polaritons which could potentially be used to experimentally test the proposed mechanism.
Wezel, Jasper van [Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE (United Kingdom)
Quantum dynamics in the thermodynamic limit
NASA Astrophysics Data System (ADS)
The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum-mechanical building blocks is one of the cornerstones of modern condensed-matter theory and has found applications in many different areas of physics. The theory of spontaneous symmetry breaking, however, is inherently an equilibrium theory, which does not address the dynamics of quantum systems in the thermodynamic limit. Here, we will use the example of a particular antiferromagnetic model system to show that the presence of a so-called thin spectrum of collective excitations with vanishing energy�one of the well-known characteristic properties shared by all symmetry-breaking objects�can allow these objects to also spontaneously break time-translation symmetry in the thermodynamic limit. As a result, that limit is found to be able, not only to reduce quantum-mechanical equilibrium averages to their classical counterparts, but also to turn individual-state quantum dynamics into classical physics. In the process, we find that the dynamical description of spontaneous symmetry breaking can also be used to shed some light on the possible origins of Born�s rule. We conclude by describing an experiment on a condensate of exciton polaritons which could potentially be used to experimentally test the proposed mechanism.
van Wezel, Jasper
Thermodynamics of Quantum Gases
NASA Astrophysics Data System (ADS)
Ultracold dilute atomic gases can be considered as model systems to address some pending problem in Many-Body physics that occur in condensed matter systems, nuclear physics, and astrophysics. We have developed a general method to probe with high precision the thermodynamics of locally homogeneous ultracold Bose and Fermi gases [1,2,3]. This method allows stringent tests of recent many-body theories. For attractive spin 1/2 fermions with tunable interaction, we will show that the gas thermodynamic properties can continuously change from those of weakly interacting Cooper pairs described by Bardeen-Cooper-Schrieffer theory to those of strongly bound molecules undergoing Bose-Einstein condensation. First, we focus on the finite-temperature Equation of State (EoS) of the unpolarized unitary gas. Surprisingly, the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid phase transition. A detailed comparison with theories including Monte-Carlo calculations has revealed some surprises and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids are directly measured for the first time. Despite orders of magnitude difference in density and temperature, our equation of state can be used to describe low density neutron matter such as the outer shell of neutron stars.[4pt] [1] S. Nascimb�ne, N. Navon, K. Jiang, F. Chevy, and C. Salomon, Nature 463, 1057 (2010)[0pt] [2] N. Navon, S. Nascimb�ne, F. Chevy, and C. Salomon, Science 328, 729 (2010)[0pt] [3] N. Navon, S. Piatecki, K. G�nter, B. Rem, T. C Nguyen, F. Chevy, W. Krauth, and C. Salomon, arXiv:1103.4449
Salomon, Christophe
Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics.
We perform a direct test of the gauge-gravity duality associated with the system of N D0-branes in type IIA superstring theory at finite temperature. Based on the fact that higher derivative corrections to the type IIA supergravity action start at the order of alpha;{'3}, we derive the internal energy in expansion around infinite 't Hooft coupling up to the subleading term with one unknown coefficient. The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) 't Hooft coupling constant. This suggests, in particular, that the open strings attached to the D0-branes provide the microscopic origin of the black hole thermodynamics of the dual geometry including alpha;{'} corrections. The coefficient of the subleading term extracted from the fit to the Monte Carlo data provides a prediction for the gravity side. PMID:19518941
Hanada, Masanori; Hyakutake, Yoshifumi; Nishimura, Jun; Takeuchi, Shingo
Quantum Maxwell's demon in thermodynamic cycles.
We study the physical mechanism of Maxwell's demon (MD), which helps do extra work in thermodynamic cycles with the heat engine. This is exemplified with one molecule confined in an infinitely deep square potential with a movable solid wall. The MD is modeled as a two-level system (TLS) for measuring and controlling the motion of the molecule. The processes in the cycle are described in a quantum fashion. It is discovered that a MD with quantum coherence or one at a temperature lower than the molecule's heat bath can enhance the ability of the whole working substance, formed by the heat engine plus the MD, to do work outside. This observation reveals that the essential role of the MD is to drive the whole working substance off equilibrium, or equivalently, to work between two heat baths with different effective temperatures. The elaborate studies with this model explicitly reveal the effect of finite size off the classical limit or thermodynamic limit, which contradicts common sense on a Szilard heat engine (SHE). The quantum SHE's efficiency is evaluated in detail to prove the validity of the second law of thermodynamics. PMID:21797303
Dong, H; Xu, D Z; Cai, C Y; Sun, C P
Quantum Maxwell's demon in thermodynamic cycles
NASA Astrophysics Data System (ADS)
We study the physical mechanism of Maxwell�s demon (MD), which helps do extra work in thermodynamic cycles with the heat engine. This is exemplified with one molecule confined in an infinitely deep square potential with a movable solid wall. The MD is modeled as a two-level system (TLS) for measuring and controlling the motion of the molecule. The processes in the cycle are described in a quantum fashion. It is discovered that a MD with quantum coherence or one at a temperature lower than the molecule�s heat bath can enhance the ability of the whole working substance, formed by the heat engine plus the MD, to do work outside. This observation reveals that the essential role of the MD is to drive the whole working substance off equilibrium, or equivalently, to work between two heat baths with different effective temperatures. The elaborate studies with this model explicitly reveal the effect of finite size off the classical limit or thermodynamic limit, which contradicts common sense on a Szilard heat engine (SHE). The quantum SHE�s efficiency is evaluated in detail to prove the validity of the second law of thermodynamics.
Dong, H.; Xu, D. Z.; Cai, C. Y.; Sun, C. P.
Thermodynamic control by frequent quantum measurements.
Heat flow between a large thermal 'bath' and a smaller system brings them progressively closer to thermal equilibrium while increasing their entropy. Fluctuations involving a small fraction of a statistical ensemble of systems interacting with the bath result in deviations from this trend. In this respect, quantum and classical thermodynamics are in agreement. Here we predict a different trend in a purely quantum mechanical setting: disturbances of thermal equilibrium between two-level systems (TLSs) and a bath, caused by frequent, brief quantum non-demolition measurements of the TLS energy states. By making the measurements increasingly frequent, we encounter first the anti-Zeno regime and then the Zeno regime (namely where the TLSs' relaxation respectively speeds up and slows down). The corresponding entropy and temperature of both the system and the bath are then found to either decrease or increase depending only on the rate of observation, contrary to the standard thermodynamical rules that hold for memory-less (Markov) baths. From a practical viewpoint, these anomalies may offer the possibility of very fast control of heat and entropy in quantum systems, allowing cooling and state purification over an interval much shorter than the time needed for thermal equilibration or for a feedback control loop. PMID:18401404
Erez, Noam; Gordon, Goren; Nest, Mathias; Kurizki, Gershon
Fundamental limitations for quantum and nanoscale thermodynamics.
The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit-when the number of particles becomes very large. Here we study thermodynamics in the opposite regime-at both the nanoscale and when quantum effects become important. Applying results from quantum information theory, we construct a theory of thermodynamics in these limits. We derive general criteria for thermodynamical state transitions, and, as special cases, find two free energies: one that quantifies the deterministically extractable work from a small system in contact with a heat bath, and the other that quantifies the reverse process. We find that there are fundamental limitations on work extraction from non-equilibrium states, owing to finite size effects and quantum coherences. This implies that thermodynamical transitions are generically irreversible at this scale. As one application of these methods, we analyse the efficiency of small heat engines and find that they are irreversible during the adiabatic stages of the cycle. PMID:23800725
Horodecki, Micha?; Oppenheim, Jonathan
Quantum collapse and the second law of thermodynamics.
A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum ratchet composed of an ensemble of pairs of interacting two-level atoms. We suggest that the measurement postulate of quantum mechanics is intricately connected to the second law of thermodynamics. More precisely, if quantum collapse is not inherently random, then the second law of thermodynamics can be violated. Our results challenge the conventional approach of simply quantifying quantum correlations as a thermodynamic work deficit. PMID:23496481
Hormoz, Sahand
-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter�antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.
Thermodynamic analysis of quantum light amplification
NASA Astrophysics Data System (ADS)
Thermodynamics of a three-level maser was studied in the pioneering work of Scovil and Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)]. In this work we consider the same three-level model, but treat both the matter and the light quantum mechanically. Specifically, we analyze an extended (three-level) dissipative (ED) Jaynes-Cummings model (JCM) within the framework of a quantum heat engine, using formulas for heat flux and power in bipartite systems introduced in our previous work [E. Boukobza and D. J. Tannor Phys. Rev. A 74, 063823 (2006)] Amplification of the selected cavity mode occurs even in this simple model, as seen by a positive steady state power. However, initial field coherence is lost, as seen by the decaying off-diagonal field density matrix elements, and by the Husimi-Kano Q function. We show that after an initial transient time the field�s entropy rises linearly during the operation of the engine, which we attribute to the dissipative nature of the evolution and not to matter-field entanglement. We show that the second law of thermodynamics is satisfied in two formulations (Clausius, Carnot) and that the efficiency of the ED JCM heat engine agrees with that defined intuitively by Scovil and Schulz-DuBois. Finally, we compare the steady state heat flux and power of the fully quantum model with the semiclassical counterpart of the ED JCM, and derive the engine efficiency formula of Scovil and Schulz-DuBois analytically from fundamental thermodynamic fluxes.
Boukobza, E.; Tannor, D. J.
Quantum Quenches in the Thermodynamic Limit
NASA Astrophysics Data System (ADS)
We introduce a linked-cluster based computational approach that allows one to study quantum quenches in lattice systems in the thermodynamic limit. This approach is used to study quenches in one-dimensional lattices. We provide evidence that, in the thermodynamic limit, thermalization occurs in the nonintegrable regime but fails at integrability. A phase transitionlike behavior separates the two regimes.
Rigol, M.
NASA Astrophysics Data System (ADS)
Part I. Second Quantization: 1. Elementary quantum mechanics; 2. Identical particles; 3. Second quantization; Part II. Examples: 4. Magnetism; 5. Superconductivity; 6. Superfluidity; Part III. Fields and Radiation: 7. Classical fields; 8. Quantization of fields; 9. Radiation and matter; 10. Coherent states; Part IV. Dissipative Quantum Mechanics: 11. Dissipative quantum mechanics; 12. Transitions and dissipation; Part V. Relativistic Quantum Mechanics: 13. Relativistic quantum mechanics; Index.
Nazarov, Yuli V.; Danon, Jeroen
Eigenstate Thermalization Hypothesis and Quantum Thermodynamics
NASA Astrophysics Data System (ADS)
One of the open questions in quantum thermodynamics reads: how can linear quantum dynamics provide chaos necessary for thermalization of an isolated quantum system? To this end, we perform an ab initio numerical analysis of a system of hard-core bosons on a lattice and show [Marcos Rigol, Vanja Dunjko & Maxim Olshanii, Nature 452, 854 (2008)] that the above controversy can be resolved via the Eigenstate Thermalization Hypothesis suggested independently by Deutsch [J. M. Deutsch, Phys. Rev. A 43, 2046 (1991)] and Srednicki [M. Srednicki, Phys. Rev. E 50, 888 (1994)]. According to this hypothesis, in quantum systems thermalization happens in each individual eigenstate of the system separately, but it is hidden initially by coherences between them. In course of the time evolution the thermal properties become revealed through (linear) decoherence that needs not to be chaotic.
Olshanii, Maxim
Introduction to Quantum Mechanics
NSDL National Science Digital Library
This text is intended for junior/senior Quantum Mechanics courses. It covers the fundamentals of quantum theory in a concise manner, covering topics from the basic formalism through perturbation theory, the adiabatic approximation, and scattering.
Griffiths, David J.
NASA Astrophysics Data System (ADS)
Gravity and quantum mechanics tend to stay out of each other's way, but this might change as we devise new experiments to test the applicability of quantum theory to macroscopic systems and larger length scales.
Amelino-Camelia, Giovanni
NSDL National Science Digital Library
This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.
Mabuchi, Hideo
NSDL National Science Digital Library
This web site contains resources for a comprehensive quantum mechanics course designed for graduate and advanced undergraduate students at Cal Tech. The course has been revised to include quantum information science, and prepares students for a course in quantum computation. Lecture notes, a syllabus, homework problems with solutions, and exam solutions are available.
Mabuchi, Hideo
Friction Force: From Mechanics to Thermodynamics
ERIC Educational Resources Information Center
We study some mechanical problems in which a friction force is acting on a system. Using the fundamental concepts of state, time evolution and energy conservation, we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws of thermodynamics and then apply them to investigate the time evolution and heat transfer of�
Ferrari, Christian; Gruber, Christian
Statistical mechanics based on fractional classical and quantum mechanics
NASA Astrophysics Data System (ADS)
The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.
Korichi, Z.; Meftah, M. T.
Thermodynamic theory of shape evolution induced by Si capping in Ge quantum dot self-assembly
NASA Astrophysics Data System (ADS)
A quantitative thermodynamic theory has been established to investigate the shape evolution mechanisms induced by Si capping in Ge quantum dot self-assembly. It was found that the decrease in Ge concentration of the quantum dot induced by Si absorption breaks the original balance of composition between the quantum dot and wetting layer. In order to create a new balance, the wetting layer is required to increase its thickness through the Ge diffusion from the quantum dot to the wetting layer, which leads to the shape evolution of the growing quantum dot. The Ge diffusion can suppress the expansion of quantum dots and promote their shrinkage. The theoretical results not only are in well agreement with the experimental observations but also reveal physical mechanisms involved in the Ge quantum dot self-assembly induced by Si capping, which implies that the established thermodynamic theory could be expected to be applicable to address the capping-assisted self-assembly of quantum dots.
Li, X. L.; Yang, G. W.
Thermodynamics of Quantum Gases for the Entire Range of Temperature
ERIC Educational Resources Information Center
We have analytically explored the thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials for the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become�
Biswas, Shyamal; Jana, Debnarayan
NASA Astrophysics Data System (ADS)
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Kapustin, Anton
Thermodynamics in solid mechanics: a commentary.
This commentary on thermodynamics in solid mechanics aims to provide an overview of the main concepts of thermodynamic processes as they apply to, and may be exploited for, studies in nonlinear solid mechanics. We give a descriptive commentary on the (physical) interpretation of these concepts, and relate these where appropriate to behaviour of solids under thermo-mechanical conditions. The motivation is firstly that students of solid mechanics have often had less exposure to thermodynamics than those in other branches of science and engineering, yet there is great value in analytical formulations of material behaviour derived from the principles of thermodynamics. It also sets the contributions in this Theme Issue in context. Along with the deliberately descriptive treatment of thermodynamics, we do outline the main mathematical statements that define the subject, knowing that full details are provided by the authors in their corresponding contributions to this issue. The commentary ends on a lighter note. In order to aid understanding and to stimulate discussion of thermodynamics in solid mechanics, we have invented a number of very basic and completely fictitious materials. These have strange and extreme behaviours that describe certain thermodynamics concepts, such as entropy, in isolation from the complexities of real material behaviour. PMID:16243702
Baker, Graham
Thermodynamics of quantum-jump-conditioned feedback control
NASA Astrophysics Data System (ADS)
We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such systems and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states.
Strasberg, Philipp; Schaller, Gernot; Brandes, Tobias; Esposito, Massimiliano
Thermodynamics of quantum-jump-conditioned feedback control.
We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such systems and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states. PMID:24483386
Strasberg, Philipp; Schaller, Gernot; Brandes, Tobias; Esposito, Massimiliano
Some Mechanical and Thermodynamical Aspects of Plasticity.
National Technical Information Service (NTIS)
Some mechanical and thermodynamical results pertaining to the behavior of a macroscopic sample of elastic-plastic material are given, as based on assumptions which idealize certain salient features of plastic flow. At the macroscopic level, a limited rang...
J. R. Rice
Supersymmetric quantum mechanics.
National Technical Information Service (NTIS)
We summarize recent developments of supersymmetric quantum mechanics. We start from the susy oscillator, mention the factorization schemes and discuss the order of levels of Schroedinger operators as an example. We mention soliton equation and the inverse...
H. Grosse
Maximum entropy production rate in quantum thermodynamics
NASA Astrophysics Data System (ADS)
In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schr�dinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible, well-behaved and intriguing, general closure of the dynamics, compatible with the nontrivial requirements of strong separability. Based on the time-energy Heisenberg uncertainty relation, we derive a lower bound to the internal-relaxation-time functionals that determine the rate of entropy generation. This bound entails an upper bound to the rate of entropy generation. By this extreme maximal-entropy-generation-rate ansatz, each indivisible subsystem follows the direction of steepest locally perceived entropy ascent at the highest rate compatible with the time- energy uncertainty principle.
Beretta, Gian Paolo
Analogy between Thermodynamics and Mechanics.
ERIC Educational Resources Information Center
Establishes and illustrates a formal analogy between the motion of a particle and the "motion" of the equilibrium state of a homogeneous system in a quasistatic process. The purpose is to show that there is a much larger set of natural coordinate transformations in thermodynamics. (GA)
Peterson, Mark A.
The Teaching of Quantum Mechanics
NSDL National Science Digital Library
This website has tips and techniques for teaching quantum mechanics. It presents and outlines central ideas in quantum mechanics and includes descriptions of textbooks and software that can be helpful in quantum classes.
Styer, Dan
Thermodynamic properties of 3-dimensional quantum antiferromagnets
NASA Astrophysics Data System (ADS)
We present systematic calculations of thermal properties of 3-dimensional quantum antiferromagnets, in the thermodynamic limit, using series expansions. For this purpose, High Temperature Expansions (HTE) are supplemented by Numerical Linked Cluster (NLC) Expansions.footnotetextR. Applegate et al, Phys. Rev. Lett. 109, 097205 (2012); R. R. P. Singh and J. Oitmaa Phys. Rev. B 85, 144414 (2012); R. R. P. Singh and J. Oitmaa Phys. Rev. B 85, 104406 (2012). These expansions provide essentially exact calculations of thermodynamic properties of the system at (i) all fields at high temperatures and (ii) at all temperatures at high fields. In addition, we show that for classical exchange spin-ice model defined on the pyrochlore lattice, the first order NLC leads to the Pauling approximation, which gives even the zero-field ground state entropy to about one percent accuracy. Thus, these calculations are accurate over a wide parameter range. Results are presented and compared with a variety of experimental systems including pyrochlore materials Yb2Ti2O7 and Er2Ti2O7 and the Hyper Kagome material Na4Ir3O8
Singh, Rajiv R. P.; Oitmaa, Jaan; Gingras, Michel J. P.
Supersymmetry in quantum mechanics
An elementary introduction is given to the subject of supersymmetry in quantum mechanics which can be understood and appreciated by any one who has taken a first course in quantum mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct n new exactly solvable Hamiltonians having n - 1, n - 2,..., 0 bound states. The relationship between the eigenvalues, eigenfunctions and scattering matrix of the supersymmetric partner potentials is derived and a class of reflectionless potentials are explicitly constructed. We extend the operator method of solving the one-dimensional harmonic oscillator problem to a class of potentials called shape-invariant potentials. It is worth emphasizing that this class includes almost all the solvable problems that are found in the standard text books on quantum mechanics. Further, we show that given any potential with at least one bound state, one can very easily construct one continuous parameter family of potentials having same eigenvalues and s-matrix. The supersymmetry inspired WKB approximation (SWKB) is also discussed and it is shown that unlike the usual WKB, the lowest order SWKB approximation is exact for the shape-invariant potentials and further, this approximation is not only exact for large quantum numbers but by construction, it is also exact for the ground state. Finally, we also construct new exactly solvable periodic potentials by using the machinery of supersymmetric quantum mechanics.
Khare, Avinash [Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, Orissa (India)
Quantum mechanics for space applications
This paper is an introduction to the following articles in the scope of quantum mechanics for space study initiated by ESA and lead by ONERA. The context of quantum mechanics for space is summarised, and the fields under development are briefly introduced. Technological applications of quantum mechanics in space are explored and some tests of quantum mechanics are outlined. We
A. Bresson; Y. Bidel; P. Bouyer; B. Leone; E. Murphy; P. Silvestrin
NSDL National Science Digital Library
The Kansas State University Visual Quantum Mechanics project is developing instructional materials about quantum physics for high school and college students. Instructional units and/or courses are being created for high school and college non-science students, pre-medical and biology students, and science and engineering majors. Each set of the teaching-learning materials integrates interactive visualizations with inexpensive materials and written documents in an activity-based environment.
Group, Kansas S.; Zollman, Dean A.
Periodic thermodynamics of isolated quantum systems.
The nature of the behavior of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient period, such a system is known to synchronize with the driving; in contrast to the nondriven case, no fundamental principle has been proposed for constructing the resulting nonequilibrium state. Here, we analytically show that, for a class of integrable systems, the relevant ensemble is constructed by maximizing an appropriately defined entropy subject to constraints, which we explicitly identify. This result constitutes a generalization of the concepts of equilibrium statistical mechanics to a class of far-from-equilibrium systems, up to now mainly accessible using ad�hoc methods. PMID:24785013
Lazarides, Achilleas; Das, Arnab; Moessner, Roderich
Periodic Thermodynamics of Isolated Quantum Systems
NASA Astrophysics Data System (ADS)
The nature of the behavior of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient period, such a system is known to synchronize with the driving; in contrast to the nondriven case, no fundamental principle has been proposed for constructing the resulting nonequilibrium state. Here, we analytically show that, for a class of integrable systems, the relevant ensemble is constructed by maximizing an appropriately defined entropy subject to constraints, which we explicitly identify. This result constitutes a generalization of the concepts of equilibrium statistical mechanics to a class of far-from-equilibrium systems, up to now mainly accessible using ad hoc methods.
Lazarides, Achilleas; Das, Arnab; Moessner, Roderich
NSDL National Science Digital Library
Visual Quantum Mechanics provides illustrations of quantum mechanics using computer-generated animations. Visualizations provide learning experiences for beginners and offer new insights to the advanced student or researcher. This project includes the development of multimedia software for teaching and scientific software for the solution of the Shrodinger equation and the visualization of these solutions in two and three dimensions. The materials presented here are related to two texts by the author. A German translation is also available. Quicktime is needed to view these movies.
Thaller, Bernd
Noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter ?, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of ? the model can be solved by using perturbation theory.
Gamboa, J.; Loewe, M.; Rojas, J. C.
Time Asymmetric Quantum Mechanics
NASA Astrophysics Data System (ADS)
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schr�dinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width ? and exponentially decaying states of lifetime ?=h/? should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0?t, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr
Biorthogonal quantum mechanics
NASA Astrophysics Data System (ADS)
The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called �biorthogonal quantum mechanics�, is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.
Brody, Dorje C.
NASA Astrophysics Data System (ADS)
The axiomatic way of teaching quantum mechanics (QM) is analyzed in the light of its effectiveness in making students ready to understand and use QM. A more intuitive method of teaching QM is proposed. An outline of how a course implementing that method could be structured is presented.
Deumens, Erik
Supersymmetric Quantum Mechanics.
National Technical Information Service (NTIS)
We give a general construction for supersymmetric Hamiltonians in quantum mechanics. We find that N-extended supersymmetry imposes very strong constraints, and for N > 4 the Hamiltonian is integrable. We give a variety of examples, for one-particle and fo...
M. de Crombrugghe V. Rittenberg
Lorentz covariant statistical mechanics and thermodynamics of the relativistic ideal gas and preferred frame
NASA Astrophysics Data System (ADS)
The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light), and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables a consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in the classical and quantum case.
Kowalski, K.; Rembieli?ski, J.; Smoli?ski, K. A.
Lorentz covariant statistical mechanics and thermodynamics of the relativistic ideal gas and preferred frame
The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light), and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables a consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in the classical and quantum case.
Kowalski, K.; Rembielinski, J.; Smolinski, K. A. [Department of Theoretical Physics, University of Lodz, ul. Pomorska 149/153, 90-236 Lodz (Poland)
Geometrizing Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.
Falciano, F. T.; Novello, M.; Salim, J. M.
Feynman's simple quantum mechanics
NASA Astrophysics Data System (ADS)
This sample class presents an alternative to the conventional introduction to quantum mechanics and describes its current use in a credit course. This alternative introduction rests on theory presented in professional and popular writings by Richard Feynman. Feynman showed that Nature gives a simple command to the electron: ``Explore all paths.'' All of nonrelativistic quantum mechanics, among other fundamental results, comes from this command. With a desktop computer the student points and clicks to tell a modeled electron which paths to follow. The computer then shows the results, which embody the elemental strangeness and paradoxical behaviors of the world of the very small. Feynman's approach requires few equations and provides a largely non-mathematical introduction to the wave function of conventional quantum mechanics. Draft software and materials already used for two semesters in an e-mail computer conference credit university course show that Feynman's approach works well with a variety of students. The sample class explores computer and written material and describes the next steps in its development.
Taylor, Edwin F.
Logical foundation of quantum mechanics
The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to adialogic semantics that is adequate in the case of a formal language for quantum physics. The system ofsequential logic which is comprised
E. W. Stachow; Theoretische Physik
Work extraction and thermodynamics for individual quantum systems.
Thermodynamics is traditionally concerned with systems comprised of a large number of particles. Here we present a framework for extending thermodynamics to individual quantum systems, including explicitly a thermal bath and work-storage device (essentially a 'weight' that can be raised or lowered). We prove that the second law of thermodynamics holds in our framework, and gives a simple protocol to extract the optimal amount of work from the system, equal to its change in free energy. Our results apply to any quantum system in an arbitrary initial state, in particular including non-equilibrium situations. The optimal protocol is essentially reversible, similar to classical Carnot cycles, and indeed, we show that it can be used to construct a quantum Carnot engine. PMID:24969511
Skrzypczyk, Paul; Short, Anthony J; Popescu, Sandu
New Formulation of Statistical Mechanics Using Thermal Pure Quantum States
NASA Astrophysics Data System (ADS)
We formulate statistical mechanics based on a pure quantum state, which we call a "thermal pure quantum (TPQ) state". A single TPQ state gives not only equilibrium values of mechanical variables, such as magnetization and correlation functions, but also those of genuine thermodynamic variables and thermodynamic functions, such as entropy and free energy. Among many possible TPQ states, we discuss the canonical TPQ state, the TPQ state whose temperature is specified. In the TPQ formulation of statistical mechanics, thermal fluctuations are completely included in quantum-mechanical fluctuations. As a consequence, TPQ states have much larger quantum entanglement than the equilibrium density operators of the ensemble formulation. We also show that the TPQ formulation is very useful in practical computations, by applying the formulation to a frustrated two-dimensional quantum spin system.
Sugiura, Sho; Shimizu, Akira
Emergent mechanics, quantum and un-quantum
NASA Astrophysics Data System (ADS)
There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications
Ralston, John P.
Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory
Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum systems. In the present contribution a simple but effective theoretical framework is introduced to clarify the connections between a purely mechanical description and the thermodynamic characterization of the equilibrium state of an isolated quantum system. A salient feature of our approach is the very transparent distinction between the statistical aspects and the dynamical aspects in the description of isolated quantum systems. Like in the classical statistical mechanics, the equilibrium distribution of any property is identified on the basis of the time evolution of the considered system. As a consequence equilibrium properties of quantum system appear to depend on the details of the initial state due to the abundance of constants of the motion in the Schroedinger dynamics. On the other hand the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. We shall consider two particular ensembles: the random pure state ensemble and the fixed expectation energy ensemble. The relation between the introduced ensembles, the properties of a given isolated system, and the standard quantum statistical description are discussed throughout the presentation. Finally we point out the conditions which should be satisfied by an ensemble in order to get meaningful thermodynamical characterization of an isolated quantum system.
Fresch, Barbara; Moro, Giorgio J. [Department of Chemical Science, University of Padova, Via Marzolo 1, Padova 35131 (Italy)
Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory
NASA Astrophysics Data System (ADS)
Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum systems. In the present contribution a simple but effective theoretical framework is introduced to clarify the connections between a purely mechanical description and the thermodynamic characterization of the equilibrium state of an isolated quantum system. A salient feature of our approach is the very transparent distinction between the statistical aspects and the dynamical aspects in the description of isolated quantum systems. Like in the classical statistical mechanics, the equilibrium distribution of any property is identified on the basis of the time evolution of the considered system. As a consequence equilibrium properties of quantum system appear to depend on the details of the initial state due to the abundance of constants of the motion in the Schr�dinger dynamics. On the other hand the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. We shall consider two particular ensembles: the random pure state ensemble and the fixed expectation energy ensemble. The relation between the introduced ensembles, the properties of a given isolated system, and the standard quantum statistical description are discussed throughout the presentation. Finally we point out the conditions which should be satisfied by an ensemble in order to get meaningful thermodynamical characterization of an isolated quantum system.
Fresch, Barbara; Moro, Giorgio J.
Existence of the thermodynamic limit for disordered quantum Coulomb systems
NASA Astrophysics Data System (ADS)
Following a recent method introduced by Hainzl, Solovej, and Lewin, we prove the existence of the thermodynamic limit for a system made of quantum electrons, and classical nuclei whose positions and charges are randomly perturbed in an ergodic fashion. All the particles interact through Coulomb forces.
Blanc, Xavier; Lewin, Mathieu
Paradigms in Physics: Thermodynamics & Statistical Mechanics Activities
NSDL National Science Digital Library
This web page provides a list of learning activities for Junior level Thermodynamics and Statistical Mechanics classes. Each activity includes a description and learning goals, guides for instructors, handouts or worksheets, and reflections of instructors who have used the activity when available. Among the topics included are entropy, Maxwell equations, PV and TS diagrams, and Legendre transforms. This material is part of the Paradigms in Physics project at Oregon State University. This work promotes the use of active student learning in upper division physics courses. Both learning materials and learning strategies are provided to help both students and instructors.
NASA Astrophysics Data System (ADS)
A human being viewing a defocused television tube with sweep voltages turned off will see point scintillations at sufficiently low intensities. We show that quantum mechanics predicts these scintillations. Furthermore, by assuming a response of the human nervous system of a type not inconsistent with experiment, measurement theory is used to show that these scintillations will be distributed in proportion to the magnitude squared of the electron wave function incident upon the television tube screen. This nervous system response is to break up the wave incident upon a spot on the retina into a number of similar waves transmitted by different nerves to the brain. The number of these waves is proportional to the incident energy density. Since the theory itself predicts the proper probability distribution, it is unnecessary to introduce a postulate for it.
Broyles, A. A.
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics. PMID:23509390
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
Hamiltonian and Thermodynamic Modeling of Quantum Turbulence
NASA Astrophysics Data System (ADS)
The state variables in the novel model introduced in this paper are the fields playing this role in the classical Landau-Tisza model and additional fields of mass, entropy (or temperature), superfluid velocity, and gradient of the superfluid velocity, all depending on the position vector and another tree dimensional vector labeling the scale, describing the small-scale structure developed in 4He superfluid experiencing turbulent motion. The fluxes of mass, momentum, energy, and entropy in the position space as well as the fluxes of energy and entropy in scales, appear in the time evolution equations as explicit functions of the state variables and of their conjugates. The fundamental thermodynamic relation relating the fields to their conjugates is left in this paper undetermined. The GENERIC structure of the equations serves two purposes: (i) it guarantees that solutions to the governing equations, independently of the choice of the fundamental thermodynamic relation, agree with the observed compatibility with thermodynamics, and (ii) it is used as a guide in the construction of the novel model.
Grmela, Miroslav
Quantum mechanics without measurements
Many of the conceptual problems students have in understanding quantum\\u000amechanics arise from the way probabilities are introduced in standard\\u000a(textbook) quantum theory through the use of measurements. Introducing\\u000aconsistent microscopic probabilities in quantum theory requires setting up\\u000aappropriate sample spaces taking proper account of quantum incompatibility.\\u000aWhen this is done the Schrodinger equation can be used to calculate\\u000aprobabilities
Robert B. Griffiths
Dissipative Forces and Quantum Mechanics
ERIC Educational Resources Information Center
Shows how to include the dissipative forces of classical mechanics in quantum mechanics by the use of non-Hermetian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. (MLH)
Eck, John S.; Thompson, W. J.
Modern Approach to Quantum Mechanics
NASA Astrophysics Data System (ADS)
Inspired by Richard Feynman and J.J. Sakurai, A Modern Approach to Quantum Mechanics lets professors expose their undergraduates to the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound. This book covers all the topics that are typically presented in a standard upper-level course in quantum mechanics, but its teaching approach is new: Rather than organizing his book according to the historical development of the field and jumping into a mathematical discussion of wave mechanics, Townsend begins his book with the quantum mechanics of spin. Thus, the first five chapters of the book succeed in laying out the fundamentals of quantum mechanics with little or no wave mechanics, so the physics is not obscured by mathematics. Starting with spin systems gives students something new and interesting while providing elegant but straightforward examples of the essential structure of quantum mechanics. When wave mechanics is introduced later, students perceive it correctly as only one aspect of quantum mechanics and not the core of the subject. Praised for its pedagogical brilliance, clear writing, and careful explanations, this book is destined to become a landmark text.
Townsend, John S.
On the Quantum Correction For Thermodynamic Equilibrium
The probability of a configuration is given in classical theory by the Boltzmann formula exp [-VhT] where V is the potential energy of this configuration. For high temperatures this of course also holds in quantum theory. For lower temperatures, however, a correction term has to be introduced, which can be developed into a power series of h. The formula is
E. P. Wigner
Thermodynamic Consistency of Mechanical Granular Theories
NASA Astrophysics Data System (ADS)
Constitutive Theories of the mechanical behaviour of soils are often derived without resort to thermodynamic considerations. The form of the closure conditions, however, needs to be in conformity with the second law of thermodynamics and depends on it, even on the particular form which the second law is postulated to take. We outline two common forms of the entropy principle, (i) due to Clausius-Duhem and exploited according to Coleman-Noll and (ii) due to I. M�ller and exploited ac- cording to Liu. We subject them to certain classes of material behaviour of saturated and unsaturated soil and show that not only the dynamic behaviour depends on the satisfaction of the second law, but equally also that in equilibrium. Examples illus- trating this will be given for (i) a dry soil with voids and exhibiting plastic internal frictional behaviour, (ii) a saturated granular fluid mixture able to model ground water soil interactions as well as (iii) a mixture of a finite number of grains with different diameters that is capable to describe inverse grading of a soil with a broad grain size distribution. In postulating constitutive relations for continuous granular mixtures, the rule of equipresence is often replaced by the rule of phase separation to simplify the com- putations. It is made plausible that, when constituents are strongly interacting, this principle is not likely to yield satisfactory formulations for the intended phenomena.
Hutter, K.
Noncommutative Quantum Mechanics and Quantum Cosmology
NASA Astrophysics Data System (ADS)
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, ? and ?. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, Jo�o Nuno
Thermodynamic properties of Th xU 1-xO 2 (0 < x < 1) based on quantum-mechanical calculations and Monte-Carlo simulations
NASA Astrophysics Data System (ADS)
Th xU 1-xO 2+y binary compositions occur in nature, uranothorianite, and as a mixed oxide nuclear fuel. As a nuclear fuel, important properties, such as the melting point, thermal conductivity, and the thermal expansion coefficient change as a function of composition. Additionally, for direct disposal of Th xU 1-xO 2, the chemical durability changes as a function of composition, with the dissolution rate decreasing with increasing thoria content. UO 2 and ThO 2 have the same isometric structure, and the ionic radii of 8-fold coordinated U 4+ and Th 4+ are similar (1.14 nm and 1.19 nm, respectively). Thus, this binary is expected to form a complete solid solution. However, atomic-scale measurements or simulations of cation ordering and the associated thermodynamic properties of the Th xU 1-xO 2 system have yet to be determined. A combination of density-functional theory, Monte-Carlo methods, and thermodynamic integration are used to calculate thermodynamic properties of the Th xU 1-xO 2 binary (? H mix, ? G mix, ? S mix, phase diagram). The Gibbs free energy of mixing (? G mix) shows a miscibility gap at equilibration temperatures below 1000 K (e.g., E exsoln = 0.13 kJ/(mol cations) at 750 K). Such a miscibility gap may indicate possible exsolution (i.e., phase separation upon cooling). A unique approach to evaluate the likelihood and kinetics of forming interfaces between U-rich and Th-rich has been chosen that compares the energy gain of forming separate phases with estimated energy losses of forming necessary interfaces. The result of such an approach is that the thermodynamic gain of phase separation does not overcome the increase in interface energy between exsolution lamellae for thin exsolution lamellae (10 �). Lamella formation becomes energetically favorable with a reduction of the interface area and, thus, an increase in lamella thickness to >45 �. However, this increase in lamellae thickness may be diffusion limited. Monte-Carlo simulations converge to an exsolved structure [lamellae || (2 1 1�)] only for very low equilibration temperatures (below room temperature). In addition to the weak tendency to exsolve, there is an ordered arrangement of Th and U in the solid solution [alternating U and Th layers || {1 0 0}] that is energetically favored for the homogeneously mixed 50% Th configurations. Still, this tendency to order is so weak that ordering is seldom reached due to kinetic hindrances. The configurational entropy of mixing (? S mix) is approximately equal to the point entropy at all temperatures, indicating that the system is not ordered.
Shuller, Lindsay C.; Ewing, Rodney C.; Becker, Udo
Classical and Quantum Mechanical Waves
NSDL National Science Digital Library
This web site consists of lecture notes in classical and quantum mechanical waves. The notes include the basics of classical waves including connections to mechanical oscillators, wave packets, and acoustic and electromagnetic waves. The final section outlines the key concepts of the quantum mechanical wave equation including probability and current, free and bound states, time dependent perturbation theory, and radiation. Visual Python and Maple animations are included for download.
Riley, Lewis
Drug-Target Binding Investigated by Quantum Mechanical/Molecular Mechanical (QM/MM) Methods
NASA Astrophysics Data System (ADS)
Many important drugs, also used in the clinics, exert their function by binding covalently to their targets. Understanding their action requires quantum mechanical simulations. Here, after briefly reviewing few basic concepts of thermodynamics and kinetics of drug-target binding, we summarize principles and applications of Car-Parrinello quantum mechanics/molecular mechanics (QM/MM) simulations. From this discussion, this approach emerges as a computational methodology particularly well suited to investigate covalent binding in systems of pharmacological relevance.
Rothlisberger, U.; Carloni, P.
Quantum Mechanics: Ontology Without Individuals
NASA Astrophysics Data System (ADS)
The purpose of the present paper is to consider the traditional interpretive problems of quantum mechanics from the viewpoint of a modal ontology of properties. In particular, we will try to delineate a quantum ontology that (i) is modal, because describes the structure of the realm of possibility, and (ii) lacks the ontological category of individual. The final goal is to supply an adequate account of quantum non-individuality on the basis of this ontology.
da Costa, Newton; Lombardi, Olimpia
Thermodynamic and quantum bounds on nonlinear dc thermoelectric transport
NASA Astrophysics Data System (ADS)
I consider the nonequilibrium dc transport of electrons through a quantum system with a thermoelectric response. This system may be any nanostructure or molecule modeled by the nonlinear scattering theory, which includes Hartree-like electrostatic interactions exactly, and certain dynamic interaction effects (decoherence and relaxation) phenomenologically. This theory is believed to be a reasonable model when single-electron charging effects are negligible. I derive three fundamental bounds for such quantum systems coupled to multiple macroscopic reservoirs, one of which may be superconducting. These bounds affect nonlinear heating (such as Joule heating), work and entropy production. Two bounds correspond to the first law and second law of thermodynamics in classical physics. The third bound is quantum (wavelength dependent), and is as important as the thermodynamic ones in limiting the capabilities of mesoscopic heat engines and refrigerators. The quantum bound also leads to Nernst's unattainability principle that the quantum system cannot cool a reservoir to absolute zero in a finite time, although it can get exponentially close.
Whitney, Robert S.
Expansion coefficients of scattering parameters in quantum thermodynamic perturbation theory
We tabulate the expansion coefficients of various scattering parameters associated with several interparticle pair potentials used in the quantum thermodynamic perturbation theory of strongly coupled, many-particle substances. The expansion is in powers or the attractive part of the pair potential. The potential is divided into repulsive and attractive parts according to several methods in vogue both in classical and in quantum equation-of-state studies of condensed-matter systems. Results are reported for several interparticle potentials of helium-3 and -4 atoms, of the three electron spin-polarized isotopes of atomic hydrogen, and of the nucleon.
Buendia, E.; Guardiola, R. (Departamento de Fisica Moderna, Universidad de Granada Granada, Spain, 18071 (ES)); De Llano, M. (Physics Department, North Dakota State University, Fargo, North Dakota 58105)
Measurement Theory in Quantum Mechanics.
National Technical Information Service (NTIS)
It is assumed that consciousness, memory and liberty (within the limits of the quantum mechanics indeterminism) are fundamental properties of elementary particles. Then, using this assumption it is shown how measurements and observers may be introduced in...
G. Klein
Quantum Mechanics of the Einstein-Hopf Model.
ERIC Educational Resources Information Center
The Einstein-Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Both the wave and particle aspects of the Einstein fluctuation formula are interpreted in terms of the fundamental absorption and emission processes. (Author/SK)
Milonni, P. W.
Dynamics and thermodynamics of linear quantum open systems.
We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities. PMID:23581302
Martinez, Esteban A; Paz, Juan Pablo
NSDL National Science Digital Library
This web site outlines a set of undergraduate physics labs that investigate quantum interference and entanglement with photons. The labs are designed for simplicity and low cost. A description of the lab set up, background information, the lab manual, and several articles on both the curriculum development and research performed in the lab are provided.
Galvez, Enrique; Holbrow, Charles
Quantum Mechanics: Fundamentals
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience.That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for
A Whitaker
ERIC Educational Resources Information Center
Discusses the quantum theory of measurement and von Neumann's catastrophe of infinite regression." Examines three ways of escapint the von Neumann catastrophe, and suggests that the solution to the dilemma of inteterminism is a universe in which all possible outcomes of an experiment actually occur. Bibliography. (LC)
DeWitt, Bryce S.
Quantum Mechanics Resource Packet
NSDL National Science Digital Library
This website contains a collection of computational resources for use in a quantum physics class. Maple files are provided to introduce students to scientific computation. This collection includes suggested problems for use with the CUPS software. Topics covered include energy levels and wave functions for various potential wells and a 1-D lattice.
Moloney, Mike; Mitra-Kirtley, Sudipa; Joenathan, Charles; Western, Arthur; Mcinerney, Michael
An Introduction to Quantum Mechanics
NSDL National Science Digital Library
This Ohio State website provides an introduction to the principles of quantum mechanics as a supplement to the "discussion of hydrogen and many-electron orbitals commonly found in general chemistry text books." Users can find informative text and graphics explaining Classical Mechanics, uncertainty, Pauli Principle, stationary states, and much more. Through the tutorial, students can explore how physical objects can be perceived as both particles and waves. With the Macromedia Shockwave plug-in, visitors can hear discussions of the quantum mechanics topics covered.
Hanlin, Heath; Kitagawa, Midori; Lilas, Zil; Mcdonald, Neal; Singer, Sherwin J. (Sherwin Jeffrey), 1954-; Timasheva, Anna
Kowalevski top in quantum mechanics
The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: �Quantum spectra of the Kowalevski top are calculated. �Semiclassical quantization is carried out by the EBK formulation. �Quantum states are labeled by the semiclassical integer quantum numbers. �Multiplicity of the classical torus makes the spectra nearly degenerate. �Symmetries, quantum numbers and near-degenerate spectra are closely related.
Matsuyama, A., E-mail: firstname.lastname@example.com
On Quantum Statistical Mechanics of a Schwarzschild Black Hole
NASA Astrophysics Data System (ADS)
Quantum theory of geometry, developed recently in the framework of non-perturbative quantum gravity, is used in an attempt to explain thermodynamics of Schwarzschild black holes on the basis of a microscopical (quantum) description of the system. We work with the formulation of thermodynamics in which the black hole is enclosed by a spherical surface B and a macroscopic state of the system is specified by two parameters: the area of the boundary surface and a quasilocal energy contained within it. To derive thermodynamical properties of the system from its microscopics we use the standard statistical mechanical method of Gibbs. Under a certain number of assumptions on the quantum behavior of the system, we find that its microscopic (quantum) states are described by states of quantum Chern-Simons theory defined by sets of points on B with spins attached. The level of the Chern-Simons theory turns out to be proportional to the horizon area of the black hole measured in Planck units. The statistical mechanical analysis turns out to be especially simple in the case when the entire interior of B is occupied by a black hole. We find in this case that the entropy contained within B, that is, the black hole entropy, is proportional to the horizon surface area.
Krasnov, Kirill V.
Quantum Mechanical Earth: Where Orbitals Become Orbits
ERIC Educational Resources Information Center
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the�
Keeports, David
Self-Referential Quantum Mechanics
NASA Astrophysics Data System (ADS)
A nonlinear quantum mechanics based upon the nonlinear logarithmic Schrodinger equation, is developed which has the property of self-reference, that is, the nonlinear term is dependent upon the square of the wavefunction. The self-referential system is examined in terms of its mathematical properties, the definition of the wavefunction, and the nonlinear system in the feedback between equation and solution. Theta operators are introduced which make possible new operations in the quantum phase. Two interpretations are presented utilizing the nonlinear quantum system: the idealistic interpretation based upon consciousness focused upon the measurement problem, and the statistical interpretation focused upon stochastic quantum fluctuations. Experimental properties are examined, beginning with a proposed analog of the Bohm-Aharonov experiment. Interference due to difference in path length for a split electron beam is effected in a region of spacetime where electromagnetic field and the vector potential are enclosed within but screened to be zero at the paths. If the wavefunction's geometrical phase contribution along the paths is different, then there should be interference induced purely by the wave-function alone. A positive result would be due to a purely wavefunction dependent effect. The spin phase of the wavefunction is postulated to be the source of the zitterbewegung of the electron. Reduction of the wavefunction in measurement is examined for self -referential quantum systems arising from consciousness and then arising from a stochastic quantum spacetime model. These results are applied to the mind-brain as a quantum processor producing a behavioral double slit experiment (ideation experiments) and nonlocal transferred potentials in an EPR-style experiment. Looking at the universe as a whole as a quantum self-referential system, leads to a modified zitterbewegung Wheeler-DeWitt equation; and, the transition from quantum-to-classical on a cosmological scale for the measurement problem is accomplished for an expanding-only deSitter quantum spacetime.
Mitchell, Mark Kenneth
Faster than Hermitian quantum mechanics.
Given an initial quantum state |psi(I)> and a final quantum state |psi(F)>, there exist Hamiltonians H under which |psi(I)> evolves into |psi(F)>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi(I)> to |psi(F)> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing. PMID:17358747
Bender, Carl M; Brody, Dorje C; Jones, Hugh F; Meister, Bernhard K
Sketching the History of Statistical Mechanics and Thermodynamics
NSDL National Science Digital Library
This site is a timeline of thermodynamics and statistical mechanics from approximately 150 BC to the present. Links to information about the people involved in the development of the field, and sources and references, are provided.
Quantum refrigerators and the third law of thermodynamics.
The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ? of the cooling process dT(t)/dt?-T^{?} when approaching absolute zero, T?0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled two-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat-driven refrigerator (absorption refrigerator) is compared to a power-driven refrigerator. When optimized, both cases lead to the same exponent ?, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined. PMID:23005070
Levy, Amikam; Alicki, Robert; Kosloff, Ronnie
Quantum Mechanics and Physical Reality
IN a recent article by A. Einstein, B. Podolsky and N. Rosen, which appeared in the Physical Review of May 15, and was reviewed in NATURE of June 22, the question of the completeness of quantum mechanical description has been discussed on the basis of a ``criterion of physical reality'', which the authors formulate as follows : ``If, without in
N. Bohr
A quantum mechanical twin paradox
When a quantummechanical wavepacket undergoes a series of Galilean boosts, the Schr�dinger theory predicts the occurrence of a geometrical phase effect that is an example of Berry's phase (Sagnac's phase). In the present paper the conceptual consequences of this phenomenon are considered, in particular for the status of Galilean invariance in nonrelativistic quantum mechanics, and for the relation between that
Dennis Dieks
A quantum mechanical twin paradox
NASA Astrophysics Data System (ADS)
When a quantummechanical wavepacket undergoes a series of Galilean boosts, the Schr�dinger theory predicts the occurrence of a geometrical phase effect that is an example of Berry's phase (Sagnac's phase). In the present paper the conceptual consequences of this phenomenon are considered, in particular for the status of Galilean invariance in nonrelativistic quantum mechanics, and for the relation between that theory and classical physics.
Dieks, Dennis
Fun with Supersymmetric Quantum Mechanics.
National Technical Information Service (NTIS)
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup alpha / for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpo...
B. Freedman F. Cooper
PT-symmetric quantum mechanics
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition H�=H on the Hamiltonian, where � represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian H has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement
Carl M. Bender; Stefan Boettcher; Peter N. Meisinger
Thermodynamics and mechanism of protonated asparagine decomposition.
Deamidation of the amino acid asparagine (Asn) is a primary route for spontaneous post-translational protein modification biologically and is a pH dependent process. Here we present a full molecular description of the deamidation and (H(2)O + CO) loss reactions of protonated asparagine, H(+)(Asn), by studying its collision-induced dissociation (CID) with Xe using a guided ion beam (GIB) tandem mass spectrometer. Analysis of the kinetic energy-dependent CID cross sections provides the 0 K barriers for the deamidation and (H(2)O + CO) loss reactions after accounting for unimolecular decay rates, internal energy of reactant ions, multiple ion-molecule collisions, and competition among the decay channels. Relaxed potential energy surface scans performed at the B3LYP/6-31G(d) level identify the transition-state (TS) and intermediate reaction species for these processes, structures that are further optimized at the B3LYP/6-311+G(d,p) level. Intrinsic reaction coordinate (IRC) calculations are also performed at this level on the rate-limiting reaction TSs to validate the molecular details and energy dependence of these species. Single point energies of the key optimized TSs and intermediates are calculated at B3LYP, B3P86, and MP2(full) levels using a 6-311+G(2d,2p) basis set. A number of alternative high-energy mechanisms for (H(2)O + CO) loss from H(+)(Asn) are also investigated. Combining both experimental work and quantum chemical calculations allows for a complete characterization of the elementary steps of these reactions as well as a comprehensive evaluation of the complex behavior of the deamidation reaction. PMID:19201618
Heaton, Amy L; Armentrout, Peter B
NASA Astrophysics Data System (ADS)
The present paper deals with three independent subjects. I. We show how for classical canonical transformation we can pass, with the help of Wigner distribution functions, from their representation U in the configurational Hilbert space to a kernel K in phase space. The latter is a much more transparent way of looking at representations of canonical transformations, as the classical limit is reached when ?-->0 and successive quantum corrections are related with powers of ?2n, n=1,2,... . II. We discuss the coherent states solution for a charged particle in a constant magnetic field and show that it is the appropriate one for getting the classical limit of the problem, i.e., motion in a circle around any point in the plane perpendicular to the field and with the square of the radius proportional to the energy of the particle. III. We show that it is possible to have just one equation involving n ?'s and ? matrices to get relativistic wave equations that can have spins with values up to n/2. We then decompose the ?'s and ?'s into direct products of ordinary spin matrices and a new type of them that we call sign spin. The problem reduces then to that of the generators of a SU(4) group, entirely similar to the one in the spin-isospin theory of nuclear physics. For a free particle of arbitrary spin the symmetry group is actually the unitary symplectic subgroup of SU(4), i.e., Sp(4). As the latter is isomorphic to O(5), we can characterize our states by the canonical chain O(5)?O(4)?O(3)?O(2), and from it obtain the spin and mass content of our relativistic equation.
Moshinsky, Marcos
Quantum mechanical evolution towards thermal equilibrium.
The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalization besides equilibration, for example, that the equilibrium state does not depend on the detailed microstate of the bath. PMID:19658469
Linden, Noah; Popescu, Sandu; Short, Anthony J; Winter, Andreas
The quantum and thermodynamical characteristics of fission taking into account adiabatic and nonadiabatic modes of motion
NASA Astrophysics Data System (ADS)
In the framework of the quantum theory of spontaneous and low-energy induced fission, the nature of quantum and thermodynamical properties of a fissioning system is analyzed taking into account adiabatic and nonadiabatic modes of motion for different fission stages. It is shown that, owing to the influence of the Coriolis interaction, the states of the fissile nucleus and of primary fission products are cold and strongly nonequilibrium. The important role of superfluid and pairing nucleon-nucleon correlations for binary and ternary fission is demonstrated. The mechanism of pumping of high values of relative orbital momenta and spins of fission fragments for binary and ternary fission and the nonevaporation mechanism of formation of third particles for ternary fission are investigated. The anisotropies and P-odd, P-even, and T-odd asymmetries for angular distributions of fission products are analyzed.
Kadmensky, S. G.
Quantum mechanics and the psyche
NASA Astrophysics Data System (ADS)
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness�i.e., that which goes together with an act or a choice�there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
Galli Carminati, G.; Martin, F.
Thermodynamics and Mechanical Equivalent of Heat
NASA Astrophysics Data System (ADS)
This paper is the first part of a three-part project `How the principle of energy conservation evolved between 1842 and 1870: the view of a participant'. This paper aims at showing how the new ideas of Mayer and Joule were received, what constituted the new theory in the period under study, and how it was supported experimentally. A connection was found between the new theory and thermodynamics which benefited both of them. Some considerations are offered about the desirability of taking a historical approach to teaching energy and its conservation.
Kipnis, Nahum
The Effects of Quantum Delocalization on the Structural and Thermodynamic Properties of Many-Body Systems
NASA Astrophysics Data System (ADS)
The following dissertation is an account of my research in the Mandelshtam group at UC Irvine beginning in the Fall of 2006 and ending in the Summer of 2011. My general area of study falls within the realm of equilibrium quantum statistical mechanics, a discipline which attempts to relate molecular-scale properties to time averaged, macroscopic observables. The major tools used herein are the Variational Gaussian Wavepacket (VGW) approximation for quantum calculations, and Monte-Carlo methods, particularly parallel tempering, for global optimization and the prediction of equilibrium thermodynamic properties. Much of my work used these two methods to model both small and bulk systems at equilibrium where quantum effects are significant. All the systems considered are characterized by inter-molecular van der Waals forces, which are weak but significant electrostatic attractions between atoms and molecules and posses a 1/r6 dependence. The research herein begins at the microscopic level, starting with Lennard-Jones (LJ) clusters, then later shifts to the macroscopic for a study involving bulk para-hydrogen. For the LJ clusters the structural transitions induced by a changing deBoer parameter, ?, a measure of quantum delocalization of the constituent particles, are investigated over a range of cluster sizes, N. From the data a "phase" diagram as a function of ? and N is constructed, which depicts the structural motifs favored at different size and quantum parameter. Comparisons of the "quantum induced" structural transitions depicted in the latter are also made with temperature induced transitions and those caused by varying the range of the Morse potential. Following this, the structural properties of binary para-Hydrogen/ ortho-Deuterium clusters are investigated using the VGW approximation and Monte-Carlo methods within the GMIN framework. The latter uses the "Basin-Hopping" algorithm, which simplifies the potential energy landscape, and coupled with the VGW approximation, an efficient and viable method for predicting equilibrium quantum mechanical properties is demonstrated. In the next chapter my contribution to the numerical implementation of the Thermal Gaussian Molecular Dynamics (TGMD) method is discussed. Within TGMD, a mapping of a quantum system to a classical is performed by means of an effective Hamiltonian, H eff, which is computed within the VGW framework. Using the classical dynamical equations of motion with Heff, the properties of a quantum system can be modeled within a classical framework. After this, the bulk system of fluid para-Hydrogen is investigated using the VGW in the NPT ensemble in an attempt to derive the thermodynamic properties at the phase transition and construct the equation of state. The dissertation then concludes with a discussion on the adaptation of the VGW methodology to any molecular system.
Deckman, Jason
Quantum mechanics on noncommutative spacetime
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect.
Calmet, Xavier; Selvaggi, Michele [Service de Physique Theorique, CP225 Boulevard du Triomphe B-1050 Brussels (Belgium)
Supersymmetric quantum mechanics with reflections
NASA Astrophysics Data System (ADS)
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q ? -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wavefunctions of extended Scarf I potentials with different parameters are presented.
Post, Sarah; Vinet, Luc; Zhedanov, Alexei
Modern Undergraduate Quantum Mechanics Experiments
NSDL National Science Digital Library
The site describes a collection of simplified quantum mechanics experiments developed at Whitman College by Professor Mark Beck. It links to a complete laboratory manual with the following experiments: (1) Spontaneous Parametric Downconversion, (2) Proof of the Existence of Photons, (3) Single Photon Interference, (4) Testing Local Realism à la Hardy. The manual also presents documentation for LabView interfaces to the experimental setups. Equipment lists, apparatus pictures, and a collection of links to additional resources is included.
Beck, Mark
Complementarity in Categorical Quantum Mechanics
NASA Astrophysics Data System (ADS)
We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a `point-free' definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras.
Heunen, Chris
Lyapounov Variable: Entropy and Measurement in Quantum Mechanics
We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantum mechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables-i.e., dynamical variables varying monotonically in time without becoming
B. Misra; I. Prigogine; M. Courbage
Faster than Hermitian Quantum Mechanics
Given an initial quantum state vertical bar {psi}{sub I}> and a final quantum state vertical bar {psi}{sub F}>, there exist Hamiltonians H under which vertical bar {psi}{sub I}> evolves into vertical bar {psi}{sub F}>. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time {tau}? For Hermitian Hamiltonians {tau} has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, {tau} can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar {psi}{sub I}> to vertical bar {psi}{sub F}> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.
Bender, Carl M. [Physics Department, Washington University, St. Louis, Missouri 63130 (United States); Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom); Brody, Dorje C. [Department of Mathematics, Imperial College, London SW7 2BZ (United Kingdom); Jones, Hugh F. [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom); Meister, Bernhard K. [Department of Physics, Renmin University of China, Beijing 100872 (China)
Helping Students Learn Quantum Mechanics for Quantum Computing
NASA Astrophysics Data System (ADS)
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.
Singh, Chandralekha
Thermodynamic and Statistical Mechanics Inconsistencies in Quasiparticle Models
NASA Astrophysics Data System (ADS)
Here we reanalyze various quasiparticle models of quark gluon plasma from the statistical mechanics and thermodynamics point of view. We investigate the statistical mechanics and thermodynamics inconsistencies involved in these models and their consequences in the observables. Quasiparticle models are phenomenological models with few parameters and by adjusting them all models fit the results of lattice gauge simulation of gluon plasma [G. Boyd et al., Phys. Rev. Lett.75, 4169 (1995); G. Boyd et al., Nucl. Phys. B469, 419 (1996)]. However, after fixing two of the three parameters of the model by physical arguments, only one quasiparticle model, which is consistent with both statistical mechanics and thermodynamics, fits the Bielefeld lattice data [G. Boyd et al., Phys. Rev. Lett.75, 4169 (1995); G. Boyd et al., Nucl. Phys. B469, 419 (1996)]. The same model also fits the recent lattice results of Wuppertal-Budapest group [S. Borsanyi et al., arXiv:1204.6184v1 [hep-lat
Bannur, Vishnu M.
Quantum mechanics and the direction of time
In recent papers the authors have discussed the dynamical properties of large Poincare systems (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. They show that this Poincare catastrophe can be eliminated by a natural time ordering of the dynamical states. They obtain then a dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that his time ordering can be performed in an extended Hilbert space. In general, they need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space.
Hasegawa, H.; Petrosky, T. (Univ. of Texas, Austin (United States)); Prigogine, I. (Univ. of Texas, Austin (United States) International Solvay Inst. for Physics and Chemistry, Brussels (Belgium)); Tasaki, S. (International Solvay Inst. for Physics and Chemistry, Brussels (Belgium))
BOOK REVIEWS: Quantum Mechanics: Fundamentals
NASA Astrophysics Data System (ADS)
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried�s well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Quantum mechanics was already solidly established by 1966, but this second edition gives an indication of progress made and changes in perspective over the last thirty-five years, and also recognises the very substantial increase in knowledge of quantum theory obtained at the undergraduate level. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Their practical importance has now been fully recognised, and a substantial account of them is provided in the new book. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. John Bell�s work of the mid-1960s has led to genuine theoretical and experimental achievement, which has facilitated the development of quantum optics and quantum information theory. Gottfried�s 1966 book played a modest part in this development. When Bell became increasingly irritated with the standard theoretical approach to quantum measurement, Viki Weisskopf repeatedly directed him to Gottfried�s book. Gottfried had devoted a chapter of his book to these matters, titled �The Measurement Process and the Statistical Interpretation of Quantum Mechanics�. Gottfried considered the von Neumann or Dirac �collapse of state-vector� (or �reduction postulate� or �projection postulate�) was unsatisfactory, as he argued that it led inevitably to the requirement to include �consciousness� in the theory. He replaced this by a more mathematically and conceptually sophisticated treatment in which, following measurement, the density matrix of the correlated measured and measuring systems, rho, is replaced by hat rho, in which the interference terms from rho have been removed. rho represents a pure state, and hat rho a mixture, but Gottfried argued that they are �indistinguishable�, and that we may make our replacement, �safe in the knowledge that the error will never be found�. Now our combined state is represented as a mixture, it is intuitive, Gottfried argued, to interpret it in a probabilistic way, |cm|2 being the probability of obtaining the mth measurement result. Bell liked Gottfried�s treatment little more than the cruder �collapse� idea of von Neumann, and when, shortly before Bell�s death, his polemical article �Against measurement� was published in the August 1990 issue of Physics World (pages 33-40), his targets included, not only Landau and Lifshitz�s classic Quantum Mechanics, pilloried for its advocacy of old-fashioned collapse, and a paper by van Kampen in Physica, but also Gottfried�s approach. Bell regarded his replacement of rho by hat rho as a �butchering� of the density matrix, and considered, in any case, that even the butchered density matrix should represent co-existence of different terms, not a set of probabilities. Gottfried has replied to Bell ( Physics World, October 1991, pages 34-40; Nature 405, 533-36 (2000)). He has also become a major commentator on Bell�s work, for example editing the section on quantum foundations in the World Scientific edition of Bell�s collected works. Thus it is exceedingly interesting to disco
Whitaker, A.
Teaching Quantum Mechanics on an Introductory Level.
ERIC Educational Resources Information Center
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Muller, Rainer; Wiesner, Hartmut
Epistemic restrictions in Hilbert space quantum mechanics
NASA Astrophysics Data System (ADS)
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results in quantum information theory. This analysis provides a quantum mechanical understanding of some recent work that shows that certain kinds of quantum behavior are exhibited by a fully classical model if by hypothesis an observer's knowledge of its state is appropriately limited.
Griffiths, Robert B.
Propagators in polymer quantum mechanics
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green�s function character. Furthermore they are also shown to reduce to the usual Schr�dinger propagators in the limit of small parameter ?{sub 0}, the length scale introduced in the polymer dynamics and which plays a role analog of that of Planck length in Quantum Gravity. -- Highlights: �Formulas for propagators of free and particle in a box in polymer quantum mechanics. �Initial conditions, composition and Green�s function character is checked. �Propagators reduce to corresponding Schr�dinger ones in an appropriately defined limit. �Results show overall consistency of the polymer framework. �For the particle in a box results are also verified using formula from method of images.
Flores-Gonz�lez, Ernesto, E-mail: email@example.com; Morales-T�cotl, Hugo A., E-mail: email@example.com; Reyes, Juan D., E-mail: email@example.com
Quantum mechanical light harvesting mechanisms in photosynthesis
NASA Astrophysics Data System (ADS)
More than 10 million billion photons of light strike a leaf each second. Incredibly, almost every red-coloured photon is captured by chlorophyll pigments and initiates steps to plant growth. Last year we reported that marine algae use quantum mechanics in order to optimize photosynthesis [1], a process essential to its survival. These and other insights from the natural world promise to revolutionize our ability to harness the power of the sun. In a recent review [2] we described the principles learned from studies of various natural antenna complexes and suggested how to utilize that knowledge to shape future technologies. We forecast the need to develop ways to direct and regulate excitation energy flow using molecular organizations that facilitate feedback and control--not easy given that the energy is only stored for a billionth of a second. In this presentation I will describe new results that explain the observation and meaning of quantum-coherent energy transfer. [4pt] [1] Elisabetta Collini, Cathy Y. Wong, Krystyna E. Wilk, Paul M. G. Curmi, Paul Brumer, and Gregory D. Scholes, ``Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature'' Nature 463, 644-648 (2010).[0pt] [2] Gregory D. Scholes, Graham R. Fleming, Alexandra Olaya-Castro and Rienk van Grondelle, ``Lessons from nature about solar light harvesting'' Nature Chem. 3, 763-774 (2011).
Scholes, Gregory
Thermodynamic Derivation of the Equilibrium Distribution Functions of Statistical Mechanics.
ERIC Educational Resources Information Center
Presents a simplified derivation of the equilibrium distribution functions. The derivation proceeds from the change in the Helmholtz free energy when a particle is added to a system of fixed temperature, volume, and chemical potential. The derivations show the relationship between statistical mechanics and macroscopic thermodynamics. (Author/GA)
Stoeckly, Beth
Quantum Mechanical Approximations in Quantum Field Theory.
National Technical Information Service (NTIS)
Some cooperative, coherent effects in quantum field theory, such as spontaneous symmetry violation, bound states, and entrapment of various excitations, can be exposed only by approximation procedures which do not rely on analyticity or regularity in the ...
R. Jackiw
Can quantum mechanics help distributed computing?
We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of quantum information significantly reduces the need for communication. The main focus of the
Anne Broadbent; Alain Tapp
Are All Probabilities Fundamentally Quantum Mechanical?
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated that all probabilities may be fundamentally quantum mechanical in the sense that they may all be derived from the corresponding amplitudes. The classical coin-toss and the quantum
Rajat Kumar Pradhan
Causality and Probability in Quantum Mechanics
NASA Astrophysics Data System (ADS)
This paper critically examines the view of quantum mechanics that emerged shortly after the introduction of quantum mechanics and that has been widespread ever since. Although N. Bohr, P. A. M. Dirac, and W. Heisenberg advanced this view earlier, it is best exemplified by J. von Neumann's argument in Mathematical Foundations of Quantum Mechanics (1932) that the transformation of ``a [quantum] state ... under the action of an energy operator ... is purely causal,'' while, ``on the other hand, the state ... which may measure a [given] quantity ... undergoes in a measurement a non-casual change.'' Accordingly, while the paper discusses all four of these arguments, it will especially focus on that of von Neumann. The paper also offers an alternative, noncausal, view of the quantum-mechanical situation and considers the differences between the ensemble and the Bayesian approaches to quantum mechanics from this perspective.
Plotnitsky, Arkady
Lyapounov variable: Entropy and measurement in quantum mechanics
We discuss the question of the dynamical meaning of the second law of thermodynamics in the framework of quantum mechanics. Previous discussion of the problem in the framework of classical dynamics has shown that the second law can be given a dynamical meaning in terms of the existence of so-called Lyapounov variables�i.e., dynamical variables varying monotonically in time without becoming contradictory. It has been found that such variables can exist in an extended framework of classical dynamics, provided that the dynamical motion is suitably unstable. In this paper we begin to extend these results to quantum mechanics. It is found that no dynamical variable with the characteristic properties of nonequilibrium entropy can be defined in the standard formulation of quantum mechanics. However, if the Hamiltonian has certain well-defined spectral properties, such variables can be defined but only as a nonfactorizable superoperator. Necessary nonfactorizability of such entropy operators M has the consequence that they cannot preserve the class of pure states. Physically, this means that the distinguishability between pure states and corresponding mixtures must be lost in the case of a quantal system for which the algebra of observables can be extended to include a new dynamical variable representing nonequilibrium entropy. We discuss how this result leads to a solution of the quantum measurement problem. It is also found that the question of existence of entropy of superoperators M is closely linked to the problem of defining an operator of time in quantum mechanics.
Misra, B.; Prigogine, I.; Courbage, M.
Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.
We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pK(a) values for almost all of the residues considered. PMID:24176005
Burger, Steven K; Schofield, Jeremy; Ayers, Paul W
Time dependent quantum thermodynamics of a coupled quantum oscillator system in a small thermal environment
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is �designed� by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of �classicalizing� behavior in the approach to thermal equilibrium are briefly considered.
Barnes, George L. [Department of Chemistry and Biochemistry, Siena College, Loudonville, New York 12211 (United States)] [Department of Chemistry and Biochemistry, Siena College, Loudonville, New York 12211 (United States); Kellman, Michael E. [Department of Chemistry and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403 (United States)] [Department of Chemistry and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403 (United States)
Time dependent quantum thermodynamics of a coupled quantum oscillator system in a small thermal environment.
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered. PMID:24320365
Barnes, George L; Kellman, Michael E
Time dependent quantum thermodynamics of a coupled quantum oscillator system in a small thermal environment
NASA Astrophysics Data System (ADS)
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.
Barnes, George L.; Kellman, Michael E.
Quantum mechanics of Proca fields
We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.
Zamani, Farhad [Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of); Mostafazadeh, Ali [Department of Mathematics, Koc University, Rumelifeneri Yolu, Sariyer, Istanbul 34450 (Turkey)
Statistical thermodynamics of quantum Brownian motion: Construction of perpetuum mobile of the second kind
The Brownian motion of a quantum particle in a harmonic confining potential and coupled to harmonic quantum thermal bath is exactly solvable. Though this system presents at high temperatures a pedagogic example to explain the laws of thermodynamics, it is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical
Th. M. Nieuwenhuizen; A. E. Allahverdyan
Quantum mechanics: A new chapter?
NASA Astrophysics Data System (ADS)
We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems, in particular the problems related to the ontological status and physical meaning of wavefunctions. It also solves the problem of non-locality. The experimental results obtained in Yves Couder's group and theoretical results by Gerdard Gr�ssing indicate that the wave-like distribution of trajectories of electrons in interference experiments are most likely due to the quantized interactions leading to a discrete set of transferred momenta. A separate experimental confirmation of this interpretation for double-slit interferometry of photons has been given by the group of Steinberg.
Hofer, Werner A.
Kindergarten Quantum Mechanics: Lecture Notes
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns 'doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I which subsumes my Logic of Entanglement. For a survey on the 'what', the 'why' and the 'hows' I refer to a previous set of lecture notes. In a last section we provide some pointers to the body of technical literature on the subject.
Coecke, Bob [Oxford University Computing Laboratory, Wolfson Building, Parks rd, OX1 3QD Oxford (United Kingdom)
Kindergarten Quantum Mechanics: Lecture Notes
NASA Astrophysics Data System (ADS)
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in [3, 4]) which subsumes my Logic of Entanglement [11]. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes [12, 13]. In a last section we provide some pointers to the body of technical literature on the subject.
Coecke, Bob
The Quantum Mechanical Many-Body Problem.
National Technical Information Service (NTIS)
A wide variety of quantum mechanical many-body problems were investigated. The two significant accomplishments of this research are as follows: The development of DCF (dynamical characteristic function) method for treating the statistical mechanics of qua...
A. E. Glassgold
Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator
NASA Astrophysics Data System (ADS)
I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.
Horowitz, Jordan M.
On a realistic interpretation of quantum mechanics
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This opens the door for an interpretation that, while respecting the indeterministic nature of quantum mechanics, allows to speak of definite values for all
Arnold Neumaier
Quantum Mechanics and physical calculations
NASA Astrophysics Data System (ADS)
We suggest to realize the computer simulation and calculation by the algebraic structure built on the basis of the logic inherent to processes in physical systems (called physical computing). We suggest a principle for the construction of quantum algorithms of neuroinformatics of quantum neural networks. The role of academician Sahakyan is emphasized in the development of quantum physics in Armenia.
Karayan, H. S.
Statistical Mechanics of Nanoscale Metallic Materials Based on Thermodynamic Availability
NASA Astrophysics Data System (ADS)
When characterizing the equilibrium behavior of small metallic systems, capillary effects can strongly influence the thermal behavior and need to be taken into account in a complete thermodynamic analysis. Although a variety of approaches have been offered to incorporate these effects, they sometimes invoke certain intensive thermodynamic quantities (e.g., chemical potentials) that are not well-defined when dealing with a physically and/or chemically inhomogeneous interfacial region.It has been proposed that many of these difficulties can be resolved by employing the thermodynamic availability function rather than the conventional free energy potentials [R.C. Cammarata, Phil Mag. 88, 927 (2008); R.C. Cammarata, Sol. State Phys. 61, 1 (2009)]. When applied to statistical mechanical calculations, capillary effects on nanoscale system behavior can be obtained in a natural and rigorous way. This procedure will be briefly reviewed and then applied to nanoscale metallic fluid and solid systems. Important issues contrasting the thermodynamic differences between fluid and solid surfaces and how they need to be included in order to obtain physically meaningful results will be discussed. Applications to gas adsorption and nucleation will be presented.
Cammarata, Robert
Polymer quantum mechanics and its continuum limit
A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model.
Corichi, Alejandro [Instituto de Matematicas, Unidad Morelia, Universidad Nacional Autonoma de Mexico, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacan 58090 (Mexico); Departamento de Gravitacion y Teoria de Campos, Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510 (Mexico); Institute for Gravitational Physics and Geometry, Physics Department, Pennsylvania State University, University Park, Pennsylvania 16802 (United States); Vukasinac, Tatjana [Facultad de Ingenieria Civil, Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Michoacan 58000 (Mexico); Zapata, Jose A. [Instituto de Matematicas, Unidad Morelia, Universidad Nacional Autonoma de Mexico, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacan 58090 (Mexico)
Quantum mechanics of open systems
NASA Astrophysics Data System (ADS)
In quantum mechanics, there is a set of problems where the system of interest interacts with another system, usually called "environment". This interaction leads to the exchange of energy and information and makes the dynamics of the system of interest essentially non-unitary. Such problems often appeared in condensed matter physics and attracted much attention after recent advances in nanotechnology. As broadly posed as they are, these problems require a variety of different approaches. This thesis is an attempt to examine several of these approaches in applications to different condensed matter problems. The first problem concerns the so-called "Master equation" approach which is very popular in quantum optics. I show that analytic properties of environmental correlators lead to strong restrictions on the applicability of the approach to the strong-coupling regime of interest in condensed matter physics. In the second problem, I use path integrals to treat the localization of particles on attractive short-range potentials when the environment produces an effective viscous friction force. I find that friction changes drastically the localization properties and leads to much stronger localization in comparison to the non-dissipative case. This has implications for the motion of heavy particles in fermionic liquids and, as will be argued below, is also relevant to the problem of high-temperature superconductivity. Finally, the third problem deals with the interplay of geometric phases and energy dissipation which occurs in the motion of vortices in superconductors. It is shown that this interplay leads to interesting predictions for vortex tunneling in high-temperature superconductors which have been partially confirmed by experiments.
Melikidze, Akakii
Nonlinear quantum mechanics: Results and open questions
NASA Astrophysics Data System (ADS)
About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schr�dinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.
Goldin, G. A.
Emergence of classical theories from quantum mechanics
NASA Astrophysics Data System (ADS)
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's "first kind of dynamics", and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.
H�j�?ek, P.
Quantum mechanics, CPT violation, and neutral kaons
NASA Astrophysics Data System (ADS)
The neutral kaon system offers a unique possibility to perform fundamental tests of the basic principles of quantum mechanics and of CPT symmetry. The most recent limits obtained by the KLOE experiment at the DA?NE e+e- collider on several kinds of possible decoherence and CPT violation mechanisms, which in some cases might be justified in a quantum gravity framework, are reviewed. No deviation from the expectations of quantum mechanics and CPT symmetry is observed, while the precision of the measurements, in some cases, reaches the interesting Planck scale region. Finally, prospects for this kind of experimental studies at KLOE-2 are presented.
Domenico, Antonio Di
An analysis of quantum effects on the thermodynamic properties of cryogenic hydrogen using the path integral method
NASA Astrophysics Data System (ADS)
In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density-temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure-volume-temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases.
Nagashima, H.; Tsuda, S.; Tsuboi, N.; Koshi, M.; Hayashi, K. A.; Tokumasu, T.
An analysis of quantum effects on the thermodynamic properties of cryogenic hydrogen using the path integral method.
In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density-temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure-volume-temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases. PMID:24712800
Nagashima, H; Tsuda, S; Tsuboi, N; Koshi, M; Hayashi, K A; Tokumasu, T
ADDENDUM: Chaos in Bohmian quantum mechanics
In our recently published paper 'Chaos in Bohmian quantum mechanics' we criticized a paper by Parmenter and Valentine (1995 Phys. Lett. A 201 1), because the authors made an incorrect calculation of the Lyapunov exponent in the case of Bohmian orbits in a quantum system of two uncoupled harmonic oscillators. After our paper was published, we became aware of an
C. Efthymiopoulos; G. Contopoulos
Improving Student Understanding of Quantum Mechanics
NASA Astrophysics Data System (ADS)
We are investigating the difficulties that students have in learning upper-level quantum mechanics and designing quantum interactive learning tutorials (QuILTs). Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. The preliminary results from the QuILTs are promising. Coauthors: Mario Belloni and Wolfgang Christian, Davidson College.
Singh, Chandralekha
Thermodynamic properties of quantum lattice models from numerical linked cluster expansions
NASA Astrophysics Data System (ADS)
We review a recently proposed numerical linked-cluster (NLC) algorithm that allows one to obtain temperature-dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. This approach provides a systematic framework to assess finite-size effects and is valid for any quantum lattice model. We present results for thermodynamic properties of spin and t-J models in different lattice geometries in two-dimensions. In addition, we present an extrapolation scheme that enables one to accelerate the convergence of NLC.
Rigol, Marcos; Singh, Rajiv R. P.
Quantum cluster equilibrium theory of liquids: molecular clusters and thermodynamics of liquid ethanol
NASA Astrophysics Data System (ADS)
Quantum cluster equilibrium (QCE) theory is presented for liquid ethanol. The cluster equilibria that dictate phase composition are determined by the rigorous techniques of quantum statistical thermodynamics in the canonical ensemble, based on the ab initio partition function. The characteristic features of the supramolecular clusters which comprise the QCE model are discussed in terms of binding energies, geometries, cooperativity and charge transfer. The validity of the resulting QCE model is demonstrated by comparison with experimental thermodynamic data: Clausius-Clapeyron pressure/temperature dependence and the specific heat. At room temperature, neat, liquid ethanol consists of approximately equal parts of monomer, cyclic tetramer and cyclic pentamer clusters.
Ludwig, R.; Weinhold, F.; Farrar, T. C.
Thermodynamic Properties of the One-Dimensional Extended Quantum Compass Model in the Presence of a Transverse Field
The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T; c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties
R. Jafari
Student difficulties in learning quantum mechanics
NSDL National Science Digital Library
Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material.
Johnston, Ian D.; Crawford, K.; Fletcher, P. R.
Student Difficulties in Learning Quantum Mechanics.
ERIC Educational Resources Information Center
Reports on a preliminary project that uses a phenomenographic approach to explore the ways in which a small number of fundamental ideas are conceptualized by students who are judged to have mastered quantum mechanics material. (DDR)
Johnston, I. D.; Crawford, K.; Fletcher, P. R.
Quantum mechanical stabilization of Minkowski signature wormholes
When one attempts to construct classical wormholes in Minkowski signature Lorentzian spacetimes violations of both the weak energy hypothesis and averaged weak energy hypothesis are encountered. Since the weak energy hypothesis is experimentally known to be violated quantum mechanically, this suggests that a quantum mechanical analysis of Minkowski signature wormholes is in order. In this note I perform a minisuperspace analysis of a simple class of Minkowski signature wormholes. By solving the Wheeler-de Witt equation for pure Einstein gravity on this minisuperspace the quantum mechanical wave function of the wormhole is obtained in closed form. The wormhole is shown to be quantum mechanically stabilized with an average radius of order the Planck length. 8 refs.
Visser, M.
SSQM (Supersymmetric Quantum Mechanics) and Nonlinear Equations.
National Technical Information Service (NTIS)
The method for obtaining the superpartner potential in the supersymmetric quantum mechanics (SSQM) is discussed in connection with the nonlinear equations and the reflectionless potentials. The correspondence between a new class of the soliton solutions t...
J. Hruby V. G. Makhan'kov
Supersymmetric Quantum Mechanics and New Potentials.
National Technical Information Service (NTIS)
Using the supersymmetric quantum mechanics the following potential are generalized. The particle in the box, Poeschl-Teller and Rosen-Morse. The new potentials are evaluated and their eigenfunctions and spectra are indicated. (Atomindex citation 20:038198...
E. Drigo Filho
Supersymmetric quantum mechanics for string-bits.
National Technical Information Service (NTIS)
The authors develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. The authors focus principally on space dimensions d = 1,2,4,8, the transverse dimensionalities of superstring in...
C. B. Thorn
Functional integral in supersymmetric quantum mechanics.
National Technical Information Service (NTIS)
The solution of the square root of the Schroedinger equation for the supersymmetric quantum mechanics is expressed in the form of series. The formula may be considered as a functional integral of the chronological exponent of the super-pseudodifferential ...
D. V. Ktitarev
Supersymmetric Quantum Mechanics of the Relativistic Particle.
National Technical Information Service (NTIS)
An alternative formulation for the superparticle in a scalar potential is presented. This method is based on a combination between the ground state wave function representation and supersymmetric quantum mechanics. For the free relativistic particle case,...
J. Gamboa J. Zanelli
Fundamental Quantum Mechanics--A Graphic Presentation
ERIC Educational Resources Information Center
Describes a presentation of basic quantum mechanics for nonscience majors that relies on a computer-generated graphic display to circumvent the usual mathematical difficulties. It allows a detailed treatment of free-particle motion in a wave picture. (MLH)
Wise, M. N.; Kelley, T. G.
Symmetry and symmetry breaking in quantum mechanics.
National Technical Information Service (NTIS)
In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels...
P. Chomaz
Using Optical Transforms To Teach Quantum Mechanics
Wave-particle duality, the superposition principle, the uncertainty principle, and single-particle interference are the most fundamental quantum mechanical concepts. The purpose of this paper is to demonstrate that these quantum mechanical principles are illuminated by a study of diffraction patterns created with laser light and a variety of two-dimensional masks. The principles of X-ray crystallography are generally taught using the Bragg
Frank Rioux; Brian J. Johnson
Noncommutative quantum mechanics from noncommutative quantum field theory.
We derive noncommutative multiparticle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously and propose a way to construct noncommutative SU(5) grand unified theory. PMID:11955188
Ho, Pei-Ming; Kao, Hsien-Chung
Macroscopic quantum mechanics in a classical spacetime.
We apply the many-particle Schr�dinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schr�dinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schr�dinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another. PMID:23679686
Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei
A Quantum Chemical Study of Bismuth Compounds Thermodynamic Properties and Configuration of Pentacoordinated Organobismuth Molecules
By the PM3 method, standard values of entropy, heats, and free energies of formation have been computed for a series of inorganic and organic bismuth compounds. Linear dependences P exper = b P theor (where P is any of the mentioned properties) have been stated, allowing a priori evaluation of thermodynamic characteristics of Bi-containing substances. A quantum chemical calculation reproduces
Alexei N. Pankratov; Inna M. Uchaeva
BOOK REVIEWS: Quantum Mechanics: Fundamentals
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text
Kurt Gottfri; Tung-Mow Yan
Quantum Mechanics, Spacetime Locality, and Gravity
NASA Astrophysics Data System (ADS)
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only one of the many, bringing an apparent arbitrariness in defining probabilities, called the measure problem. In this paper, we discuss how these two problems are related with each other, developing a picture for quantum measurement and cosmological histories in the quantum mechanical universe. In order to describe the cosmological dynamics correctly within the full quantum mechanical context, we need to identify the structure of the Hilbert space for a system with gravity. We argue that in order to keep spacetime locality, the Hilbert space for dynamical spacetime must be defined only in restricted spacetime regions: in and on the (stretched) apparent horizon as viewed from a fixed reference frame. This requirement arises from eliminating all the redundancies and overcountings in a general relativistic, global spacetime description of nature. It is responsible for horizon complementarity as well as the "observer dependence" of horizons/spacetime�these phenomena arise to represent changes of the reference frame in the relevant Hilbert space. This can be viewed as an extension of the Poincar� transformation in the quantum gravitational context. Given an initial condition, the evolution of the multiverse state obeys the laws of quantum mechanics�it evolves deterministically and unitarily. The beginning of the multiverse, however, is still an open issue.
Nomura, Yasunori
Can quantum mechanics and supersymmetric quantum mechanics be the multidimensional Ermakov theories?
NASA Astrophysics Data System (ADS)
For both the Schr�dinger equation in quantum mechanics and the Riccati-type equation satisfied by the superpotential in supersymmetric quantum mechanics, we explicitly show that there exists an Ermakov-type functional invariant with respect to the space variable. An energy-like interpretation is suggested for this invariant.
Kaushal, R. S.; Parashar, D.
Optimal guidance law in quantum mechanics
Following de Broglie�s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle�s motion is just the wavefunction ?(t,x), a solution to the Schr�dinger equation; meanwhile, the closed-loop guidance system forms a complex state�space dynamics for ?(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function ?{sup ?}?. -- Highlights: �Treating quantum mechanics as a pursuit-evasion game. �Reveal an interesting analogy between guided flight motion and guided quantum motion. �Solve optimal quantum guidance problem by dynamic programming. �Gives a formal proof of de Broglie�Bohm�s idea of a pilot wave. �The optimal pilot wave is shown to be a wavefunction solved from Schr�dinger equation.
Yang, Ciann-Dong, E-mail: firstname.lastname@example.com; Cheng, Lieh-Lieh, E-mail: firstname.lastname@example.com
Emergent quantum mechanics of finances
NASA Astrophysics Data System (ADS)
This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price�time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed.
Nastasiuk, Vadim A.
a Proper Nonlocal Formulation of Quantum Maximum Entropy Principle in Statistical Mechanics
NASA Astrophysics Data System (ADS)
By considering Wigner formalism, the quantum maximum entropy principle (QMEP) is here asserted as the fundamental principle of quantum statistical mechanics when it becomes necessary to treat systems in partially specified quantum states. From one hand, the main difficulty in QMEP is to define an appropriate quantum entropy that explicitly incorporates quantum statistics. From another hand, the availability of rigorous quantum hydrodynamic (QHD) models is a demanding issue for a variety of quantum systems. Relevant results of the present approach are: (i) The development of a generalized three-dimensional Wigner equation. (ii) The construction of extended quantum hydrodynamic models evaluated exactly to all orders of the reduced Planck constant ?. (iii) The definition of a generalized quantum entropy as global functional of the reduced density matrix. (iv) The formulation of a proper nonlocal QMEP obtained by determining an explicit functional form of the reduced density operator, which requires the consistent introduction of nonlocal quantum Lagrange multipliers. (v) The development of a quantum-closure procedure that includes nonlocal statistical effects in the corresponding quantum hydrodynamic system. (vi) The development of a closure condition for a set of relevant quantum regimes of Fermi and Bose gases both in thermodynamic equilibrium and nonequilibrium conditions.
Trovato, M.; Reggiani, L.
Thermodynamics and Statistical Mechanics of Bulk Metallic Glasses
NASA Astrophysics Data System (ADS)
A survey of the mechanical, rheological, and thermodynamic properties of bulk metallic glasses and glass forming liquids will be presented. The experimental data reveal striking systematic correlations among linear elastic constants, plastic yielding of the glass and its dependence on temperature, the glass transition temperature, and rheological properties of the glass forming liquid. A Cooperative Shear Model will be presented while predicts that physically relevant features of the Potential Energy Landscape of the glass/liquid obey simple scaling relations. The model predicts the yield criterion and its dependence on temperature in the glass. It also leads to natural expressions for the Newtonian and Non-Newtonian viscosity law for the liquids, as well as the fragility of the liquid. The model is found to be in remarkable agreement with a variety of experimental observations including variations in ductility and toughness among metallic glasses. It predicts that all metallic glasses exhibit universal behavior based on a small number of measurable parameters.
Johnson, William L.
Mechanics and chemical thermodynamics of a temperature-sensitive hydrogel
NASA Astrophysics Data System (ADS)
A temperature-sensitive hydrogel is a network of polymers containing monomers, whose interaction with water molecules can be tuned dramatically by changing temperature. In most cases, the swelling ratio of a temperature-sensitive hydrogel changes discontinuously upon heating above or cooling below a critical temperature, which is called volume phase transition. Interestingly, the coexistence of swollen phases and shrunk phases are frequently observed in the experiments for temperature-sensitive hydrogels and additionally, people have also discovered that a uniaxial force can induce phase transition in a temperature-sensitive gel bar .In order to understand these phenomena, we studied the mechanics and chemical thermodynamics of a temperature-sensitive hydrogel bar, by using the free-energy landscape of a bar made from PNIPAM gel. Following Gibbs, we plot the phase diagram of a temperature-sensitive hydrogel bar under uniaxial force.
Cai, Shengqiang; Suo, Zhigang
Thermodynamic mechanism for the evasion of antibody neutralization in flaviviruses.
Mutations in the epitopes of antigenic proteins can confer viral resistance to antibody-mediated neutralization. However, the fundamental properties that characterize epitope residues and how mutations affect antibody binding to alter virus susceptibility to neutralization remain largely unknown. To address these questions, we used an ensemble-based algorithm to characterize the effects of mutations on the thermodynamics of protein conformational fluctuations. We applied this method to the envelope protein domain III (ED3) of two medically important flaviviruses: West Nile and dengue 2. We determined an intimate relationship between the susceptibility of a residue to thermodynamic perturbations and epitope location. This relationship allows the successful identification of the primary epitopes in each ED3, despite their high sequence and structural similarity. Mutations that allow the ED3 to evade detection by the antibody either increase or decrease conformational fluctuations of the epitopes through local effects or long-range interactions. Spatially distant interactions originate in the redistribution of conformations of the ED3 ensembles, not through a mechanically connected array of contiguous amino acids. These results reconcile previous observations of evasion of neutralization by mutations at a distance from the epitopes. Finally, we established a quantitative correlation between subtle changes in the conformational fluctuations of the epitope and large defects in antibody binding affinity. This correlation suggests that mutations that allow viral growth, while reducing neutralization, do not generate significant structural changes and underscores the importance of protein fluctuations and long-range interactions in the mechanism of antibody-mediated neutralization resistance. PMID:24950171
Maillard, Rodrigo A; Liu, Tong; Beasley, David W C; Barrett, Alan D T; Hilser, Vincent J; Lee, J Ching
Superstrings and the Foundations of Quantum Mechanics
NASA Astrophysics Data System (ADS)
It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.
't Hooft, Gerard
Superstrings and the Foundations of Quantum Mechanics
NASA Astrophysics Data System (ADS)
It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell's powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.
't Hooft, Gerard
Space and time from quantum mechanics
Classical mechanics historically preceded quantum mechanics and thus far has not been displaced from primary status; the path to construction of quantum theory has remained rooted in classical ideas about objective reality within space and time. Use of a less correct theory as underpinning for a more correct theory not only is unaesthetic but has spawned the perplexing and never-resolved puzzle of measurement. A growing number of physicist-philosophers torture themselves these days over collapse of the quantum-mechanical state vector when measurement is performed. Additionally, pointlike structure of the spacetime manifold underlying local classical fields has endowed quantum theory with mathematical dilemmas. It has been proposed by Gell-Mann and Hartle that objectively-realistic ideas such as measurement may lack a priori status, the predominantly classical present universe having evolved as a relic of the big bang. Other authors have suggested that spacetime itself need not be a priori but may stem from quantum mechanics. Haag has written recently that spacetime without (quantum) events is probably a meaningless concept. Henry Stapp and I have for several years been exploring a simple quantum system devoid of classical underpinning, even spacetime, but admitting within the Hilbert space a special Lie-group-related category of vector known as coherent state. Groups unitarily representable in our Hilbert space include the Poincare group, which relates to 3 + 1 spacetime. Coherent states generally are labeled by parameters associated with unitary group representations, and it has long been recognized that when such parameters become large a classical objective interpretation may result. Stapp and I have been attempting to understand space and time via large coherent-state parameters. Six years ago I presented to this gathering a preliminary report on our enterprise; in this paper I provide an update.
Chew, G.F.
Thermodynamic model of metal-induced self-assembly of Ge quantum dots on Si substrates
NASA Astrophysics Data System (ADS)
We have investigated the nucleation thermodynamics and kinetics of the Ge quantum dot (QD) self-assembly on the Au-patterned Si substrates based on the surface chemical potential theory. It is find that the minimum chemical potential on the substrate surface is located at the center site of the square lattice constructed by Au islands, which indicates that the nucleation of QD is thermodynamically favorable at the center site. The nucleation probability of QD at the center site is kinetically calculated by the mechanochemical potential-based approach. The influence of the surface orientation of Si substrates on the QD shape is addressed by the surface chemical potential theory.
Li, X. L.; Ouyang, G.; Yang, G. W.
Towards polymer quantum mechanics for fermionic systems
NASA Astrophysics Data System (ADS)
Polymer quantum mechanics is based on models that mimic the loop quantization of gravity. It coincides with the results of the standard quantum mechanical treatment for such models when a certain length scale parameter is considered to be small. In this work we present some steps in the construction of the polymer representation of a Fermi oscillator, the fermonic counterpart of the harmonic oscillator. It is suggested that the non regular character of the bosonic polymer representation has as a counterpart the non superanalytic character of the fermonic polymer case. We propose a candidate Hamiltonian operator and investigate and contrast its energy spectrum with the standard one.
Garc�a-Chung, Angel A.; Morales-T�cotl, Hugo A.; Reyes, Juan D.
Two basic Uncertainty Relations in Quantum Mechanics
NASA Astrophysics Data System (ADS)
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schr�dinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
Angelow, Andrey
DFT investigation of the thermodynamics and mechanism of electrophilic chlorination and iodination of arenes.
Quantum chemical calculations at the B3LYP/6-311G level have been carried out in order to investigate the reaction mechanisms of the iodination of benzene and its monosubstituted derivatives with ICl, I(+), I (3) (+) and reagents containing N-I and O-I bonds as the iodinating agents. The results are compared with those obtained for chlorination by Cl(+) and Cl(2), both in the gas phase and in methanol solution using the PCM solvent model. We have also used the MP2/DGDZVP level of theory and the IEFPCM model to perform comparisons in a few cases. The thermodynamic parameters for the reactions have been calculated, the structures of the intermediate products (?- and ?-complexes) and transition states have been optimized, and the profiles of the free energy surfaces have been constructed. PMID:21279527
Filimonov, Victor D; Poleshchuk, Oleg Kh; Krasnokutskaya, Elena A; Frenking, Gernot
Thermodynamics of quadrature trajectories in open quantum systems
NASA Astrophysics Data System (ADS)
We apply a large-deviation method to study the diffusive trajectories of the quadratures of light emitted from open quantum systems. We formulate the study of quadrature trajectories in terms of characteristic operators and show that, in the long-time limit, the statistics of such trajectories obey a large-deviation principle. We take our motivation from homodyne detection schemes which allow the statistics of light quadratures to be measured. We illustrate our approach with four examples of increasing complexity: a driven two-level system, a �blinking� three-level system, a pair of weakly coupled two-level driven systems, and the micromaser. We discuss how quadrature operators can serve as alternative order parameters for the classification of dynamical phases, which is particularly useful in cases where the statistics of quantum jumps cannot distinguish such phases. The formalism we introduce also allows us to analyze the properties of the light emitted in quantum-jump trajectories which deviate far from the typical dynamics.
Hickey, James M.; Genway, Sam; Lesanovsky, Igor; Garrahan, Juan P.
Relating the Quantum Mechanics of Discrete Systems to Standard Canonical Quantum Mechanics
NASA Astrophysics Data System (ADS)
Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators and , to systems with real-valued canonical coordinates and their associated momentum operators . The discrete system could be entirely deterministic while the corresponding ( p, q) system could still be typically quantum mechanical.
't Hooft, Gerard
A Theory of Quantum Gravity may not be possible because Quantum Mechanics violates the Equivalence Principle
Quantum mechanics clearly violates the weak equivalence principle (WEP). This implies that quantum mechanics also violates the strong equivalence principle (SEP), as shown in this paper. Therefore a theory of quantum gravity may not be possible unless it is not based upon the equivalence principle, or if quantum mechanics can change its mass dependence. Neither of these possibilities seem likely
Mario Rabinowitz
Ultrafast Quantum Mechanics/Molecular Mechanics Monte Carlo simulations using generalized multipole polarizabilities
NASA Astrophysics Data System (ADS)
A fast and accurate Quantum Mechanics/Molecular Mechanics method is described for thermodynamic simulation of solutes (or active sites in flexible molecules) in polar environments. The solute is described quantum mechanically and is held fixed during averaging over solvent configurations, which are described by Molecular Mechanics. Quantum calculations during simulation are replaced by the evaluation of the response of the solute to the long range electric field of the solvent, using precalculated generalized electric moments and polarizabilities. This results in huge decrease of computational time without affecting the accuracy of the QM/MM results. Implementation in a Monte Carlo program accelerated the simulations of guanine and the phenylalanine dipeptide in TIP3P water by over four orders of magnitude. Polarizability is essential for accuracy. Its inclusion decreases the average signed energy error and its standard deviation from 5.69 to 0.003 and 1.22 to 0.013 kcal/mol, respectively, for the dipeptide. Hyperpolarizability contributions are insignificant.
Janowski, Tomasz; Wolinski, Krzysztof; Pulay, Peter
Quantum statistics and thermodynamics in the harmonic approximation
NASA Astrophysics Data System (ADS)
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies enter. The number of states of given energy and symmetry is found by separating the center-of-mass motion, and by counting the remaining states of given symmetry and excitation energy of the relative motion. The oscillator frequencies that enter the harmonic Hamiltonian can be derived from realistic model parameters, and the method corresponds to an effective interaction approach based on harmonic interactions. To demonstrate the method, we apply it to systems in two dimensions. Numerical calculations are compared to a brute force method, which is considerably more computationally intensive.
Armstrong, J. R.; Zinner, N. T.; Fedorov, D. V.; Jensen, A. S.
Variational cluster approximation to the thermodynamics of quantum spin systems
NASA Astrophysics Data System (ADS)
We derive a variational cluster approximation for Heisenberg spin systems at finite temperature based on the ideas of the self-energy functional theory by Potthoff for fermionic and bosonic systems with local interactions. Partitioning the real system into a set of clusters, we find an analytical expression for the auxiliary free energy, depending on a set of variational parameters defined on the cluster, whose stationary points provide approximate solutions from which the thermodynamics of spin models can be obtained. We explicitly describe the technical details of how to evaluate the free energy for finite clusters and remark on specific problems and possible limitations of the method. To test the approximation we apply it to the antiferromagnetic spin 1/2 chain and compare the results for varying cluster sizes and choices of variational parameters with the exact Bethe ansatz solution.
Filor, S.; Pruschke, T.
Can quantum mechanics fool the cosmic censor?
NASA Astrophysics Data System (ADS)
We revisit the mechanism for violating the weak cosmic-censorship conjecture (WCCC) by overspinning a nearly-extreme charged black hole. The mechanism consists of an incoming massless neutral scalar particle, with low energy and large angular momentum, tunneling into the hole. We investigate the effect of the large angular momentum of the incoming particle on the background geometry and address recent claims that such a backreaction would invalidate the mechanism. We show that the large angular momentum of the incident particle does not constitute an obvious impediment to the success of the overspinning quantum mechanism, although the induced backreaction turns out to be essential to restoring the validity of the WCCC in the classical regime. These results seem to endorse the view that the �cosmic censor� may be oblivious to processes involving quantum effects.
Matsas, G. E. A.; Richartz, M.; Saa, A.; da Silva, A. R. R.; Vanzella, D. A. T.
Relativistic quantum mechanics of supersymmetric particles
The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge sypersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist.
Marc Henneaux; Claudio Teitelboim
Student Difficulties with Quantum Mechanics Formalism
NSDL National Science Digital Library
We discuss student difficulties in distinguishing between the physical space and Hilbert space and difficulties related to the Time-independent Schroedinger equation and measurements in quantum mechanics. These difficulties were identified by administering written surveys and by conducting individual interviews with students.
Singh, Chandralekha
Finite Size Scaling in Quantum Mechanics
The finite size scaling ansatz is combined with the variational method to extract information about critical behavior of quantum Hamiltonians. This approach is based on taking the number of elements in a complete basis set as the size of the system. As in statistical mechanics, the finite size scaling can then be used directly in the Schrodinger equation. This approach
Pablo Serra; Juan Pablo Neirotti; Sabre Kais
Quantum mechanical hamiltonian models of turing machines
Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1\\/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both
Paul Benioff
Spacetime Probabilities in Nonrelativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
We demonstrate the existence of spacetime probabilities in nonrelativistic quantum mechanics, that is, quantum mechanical probabilities for a set of alternatives which are associated, not with a surface of constant time, but with spacetime domains with nonzero spatial and temporal width in Newtonian spacetime. We use the criterion that quantum mechanical probabilities can be defined for a set of alternatives if and only if the interference between any two different alternatives vanishes. Although generalized quantum mechanics was formulated on the basis of this criterion, the actual existence of spacetime probabilities has not been known. In this paper we consider a rectangular spacetime domain Omega and introduce a set of spacetime alternatives \\{Yes, No\\}: ``Yes'' is to find a particle in Omega and ``No'' is the complement to ``Yes''. We show that, if the initial amplitude of the particle belongs to a specific class, then the criterion of vanishing interference is met by ``Yes'' and ``No'' and spacetime probabilities can be therefore defined for the set \\{Yes, No\\}. Owing to the property of the initial amplitude belonging to the class, the resultant probabilities are associated with a clear measurement theoretical meaning.
Yamada, N.; Takagi, S.
Understanding Kinetic Energy paradox in Quantum Mechanics
A concept of Kinetic Energy in Quantum Mechanics is analyzed. Kinetic Energy is not zero in many cases where there are no motion and flux. This paradox can be understood, using expansion of the wave function in Fourier integral, that is on the basis of virtual plane waves.
Yuri Kornyushin
Kinetic and electrostatic energies in quantum mechanics
A concept of kinetic energy in quantum mechanics is analyzed. Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be understood, using expansion of the wave function into Fourier integral, that is, on the basis of virtual plane
Yuri Kornyushin
Application of nonstandard analysis to quantum mechanics
Quantum mechanics is formulated using a nonstandard Hilbert space. The concept of an eigen vector of a linear operator, which applies to standard as well as nonstandard Hilbert spaces, is replaced by the more general concept of an ultra eigen vector, which applies to nonstandard Hilbert spaces alone. Ultra eigen vectors corresponding to all spectral points of internal self?adjoint operators
M. O. Farrukh
Inverse scattering with supersymmetric quantum mechanics
The application of supersymmetric quantum mechanics to the inverse scattering problem is reviewed. The main difference with standard treatments of the inverse problem lies in the simple and natural extension to potentials with singularities at the origin and with a Coulomb behaviour at infinity. The most general form of potentials which are phase-equivalent to a given potential is discussed. The
Daniel Baye; Jean-Marc Sparenberg
Solution for quantum mechanical problem in physics
NASA Astrophysics Data System (ADS)
The Schr�dinger equation is the fundamental equation of physics for describing quantum mechanical behavior. In this Paper the solution is obtained by Variational Homotopy perturbation method which is coupling of Variational iteration method and Homotopy Perturbation Method. The solution describes how the wave function of a physical system evolves over time.
Daga, Amruta; Pradhan, V. H.
Thermodynamically stable dispersions of quantum dots in a nematic liquid crystal.
Using transmittance electron microscopy, fluorescence and polarizing optical microscopy, optical spectroscopy, and fluorescent correlation spectroscopy, it was shown that CdSe/ZnS quantum dots coated with a specifically designed surfactant were readily dispersed in nematic liquid crystal (LC) to form stable colloids. The mixture of an alkyl phosphonate and a dendritic surfactant, where the constituent molecules contain promesogenic units, enabled the formation of thermodynamically stable colloids that were stable for at least 1 year. Stable colloids are formed due to minimization of the distortion of the LC ordering around the quantum dots. PMID:23808380
Prodanov, Maksym F; Pogorelova, Nataliya V; Kryshtal, Alexander P; Klymchenko, Andrey S; Mely, Yves; Semynozhenko, Vladimir P; Krivoshey, Alexander I; Reznikov, Yurii A; Yarmolenko, Sergey N; Goodby, John W; Vashchenko, Valerii V
Riemann hypothesis and quantum mechanics
NASA Astrophysics Data System (ADS)
In their 1995 paper, Jean-Beno�t Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ?(?), where ? is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low-temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written as \\phi _{\\beta }(q)=N_{q-1}^{\\beta -1} \\psi _{\\beta -1}(N_q), where Nq = ?qk = 1pk is the primorial number of order q and ?b is a generalized Dedekind ? function depending on one real parameter b as \\psi _b (q)=q \\prod _{p \\in {P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}. Fix a large inverse temperature ? > 2. The RH is then shown to be equivalent to the inequality N_q |\\phi _\\beta (N_q)|\\zeta (\\beta -1) \\gt e^\\gamma log log N_q, for q large enough. Under RH, extra formulas for high-temperature KMS states (1.5 < ? < 2) are derived. 'Number theory is not pure Mathematics. It is the Physics of the world of Numbers.' Alf van der Poorten
Planat, Michel; Sol�, Patrick; Omar, Sami
Consistent interpretations of quantum mechanics
Within the last decade, significant progress has been made towards a consistent and complete reformulation of the Copenhagen interpretation (an interpretation consisting in a formulation of the experimental aspects of physics in terms of the basic formalism; it is consistent if free from internal contradiction and complete if it provides precise predictions for all experiments). The main steps involved decoherence (the transition from linear superpositions of macroscopic states to a mixing), Griffiths histories describing the evolution of quantum properties, a convenient logical structure for dealing with histories, and also some progress in semiclassical physics, which was made possible by new methods. The main outcome is a theory of phenomena, viz., the classically meaningful properties of a macroscopic system. It shows in particular how and when determinism is valid. This theory can be used to give a deductive form to measurement theory, which now covers some cases that were initially devised as counterexamples against the Copenhagen interpretation. These theories are described, together with their applications to some key experiments and some of their consequences concerning epistemology.
Omnes, R. (Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris XI, Batiment 211, 91405 Orsay CEDEX (France))
A probabilistic approach to quantum mechanics based on tomograms
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function
Michele Caponigro; Stefano Mancini; V. I. Man'ko
Control of quantum thermodynamic behavior of a charged magneto-oscillator with momentum dissipation
NASA Astrophysics Data System (ADS)
In this work we expose the role of environment, confinement, and external magnetic field B in determining the low-temperature thermodynamic behavior in the context of cyclotron motion of a charged oscillator with anomalous dissipative coupling involving momentum instead of the much studied coordinate coupling. Explicit expressions for different quantum thermodynamic functions (QTFs) are obtained at low temperatures for different quantum heat baths characterized by the spectral density function ? (?). The power-law fall of different QTFs is in conformity with the third law of thermodynamics; however, the sensitivity of decay, i.e., the power of the power-law decay, explicitly depends on ? (?). We also discuss separately the influence of confinement and magnetic field on the low-temperature behavior of different QTFs. In this process we demonstrate how to control the low-temperature behavior of anomalous dissipative quantum systems by varying the confining length a, B, and the temperature T. Momentum dissipation reduces the effective mass of the system and we also discuss its effect on different QTFs at low temperatures.
Rajesh, Asam; Bandyopadhyay, Malay
Thermodynamic limits to the efficiency of solar energy conversion by quantum devices
NASA Technical Reports Server (NTRS)
The second law of thermodynamics imposes a strict limitation to the energy converted from direct solar radiation to useful work by a quantum device. This limitation requires that the amount of energy converted to useful work (energy in any form other than heat) can be no greater than the change in free energy of the radiation fields. Futhermore, in any real energy conversion device, not all of this available free energy in the radiation field can be converted to work because of basic limitations inherent in the device itself. A thermodynamic analysis of solar energy conversion by a completely general prototypical quantum device is presented. This device is completely described by two parameters, its operating temperature T sub R and the energy threshold of its absorption spectrum. An expression for the maximum thermodynamic efficiency of a quantum solar converter was derived in terms of these two parameters and the incident radiation spectrum. Efficiency curves for assumed solar spectral irradiance corresponding to air mass zero and air mass 1.5 are presented.
Buoncristiani, A. M.; Byvik, C. E.; Smith, B. T.
Nonadiabatic Transitions in Exactly Solvable Quantum Mechanical Multichannel Model: Role of Level Curvature and Counterintuitive Behavior
NASA Astrophysics Data System (ADS)
We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. In the limit N?1, where N is the number of states, we find that the survival probability of the initially populated state remains finite despite an almost arbitrary choice of a large number of parameters. This observation proves that quantum mechanical nonadiabatic transitions among a large number of states can effectively keep memory about the initial state of the system. This property can lead to a strongly nonergodic behavior even in the thermodynamic limit of some systems with a broad distribution of coupling constants and the lack of energy conservation.
Sinitsyn, N. A.
Quantum mechanical coherence, resonance, and mind
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Stapp, H.P.
Np Incorporation into Uranyl Alteration Phases: A Quantum Mechanical Approach
Neptunium is a major contributor to the long-term radioactivity in a geologic repository for spent nuclear fuel (SNF) due to its long half-life (2.1 million years). The mobility of Np may be decreased by its incorporation into the U{sup 6+} phases that form during the corrosion of SNF. The ionic radii of Np{sup 5+} (0.089 nm) and U{sup 6+} (0.087 nm) are similar, as is their chemistry. Experimental studies have shown that Np can be incorporated into uranyl phases up to concentrations on the order of 100 ppm. The low concentration of Np in the uranyl phases complicates experimental detection and presents a significant challenge for determining the incorporation mechanism. Therefore, we have used quantum mechanical calculations to investigate incorporation mechanisms and evaluate the energetics of Np substituting for U. CASTEP, a density functional theory based code that uses plane waves to model the behavior of the valence electrons and pseudo-potentials to model the behavior of the core and inner valence electrons, was used to calculate optimal H positions, relaxed geometry, and the energy of different uranyl phases. The incorporation energy for Np into uranyl alteration phases was calculated for studtite, [(UO{sub 2})O{sub 2}(H{sub 2}O){sub 2}](H{sub 2}O){sub 2}, and boltwoodite, HK(UO{sub 2})(SiO{sub 4}) 1.5(H{sub 2}O). Studtite is the rare case of a stable, naturally-occurring peroxide mineral, in this case a uranyl hydroxyl peroxide that forms in the presence of H{sub 2}O{sub 2} from the radiolysis of H{sub 2}O. For studtite, two incorporation mechanisms were evaluated: (1) charge-balanced substitution of Np{sup 5+} and H{sup +} for one U{sup 6+}, and (2) direct substitution of Np{sup 6+} for U{sup 6+}. For boltwoodite, the H atomic positions prior to Np incorporation were determined, as well as the Np incorporation mechanisms and the corresponding substitution energies. The preferential incorporation of Np into different structure types of U{sup 6+} minerals was also investigated. Quantum mechanical substitution energies have to be derived at Np concentrations higher than the ones found in experiments or expected in a repository in order to avoid the calculation of unit cells that are too large to be handled quantum mechanically. However, the quantum mechanical results are crucial for subsequent empirical force-field and Monte-Carlo simulations to determine the thermodynamically stable limit of Np incorporation into these uranyl phases. (authors)
Shuller, Lindsay [Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109 (United States); Ewing, Rodney C. [Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109 (United States)]|[Department of Geological Sciences, University of Michigan, Ann Arbor, MI, 48109 (United States); Becker, Udo [Department of Geological Sciences, University of Michigan, Ann Arbor, MI, 48109 (United States)
The emergent Copenhagen interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR�Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.
Hollowood, Timothy J.
Emerging interpretations of quantum mechanics and recent progress in quantum measurement
NASA Astrophysics Data System (ADS)
The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).
Clarke, M. L.
Electronic, mechanical, and thermodynamic properties of americium dioxide
NASA Astrophysics Data System (ADS)
By performing density functional theory (DFT) +U calculations, we systematically study the electronic, mechanical, tensile, and thermodynamic properties of AmO2. It is found that the chemical bonding character in AmO2 is similar to that in PuO2, with smaller charge transfer and stronger covalent interactions between americium and oxygen atoms. The stress-strain relationship of AmO2 is examined along the three low-index directions, showing that the [1 0 0] and [1 1 1] directions are the strongest and weakest tensile directions, respectively, but the theoretical tensile strengths of AmO2 are smaller than those of PuO2. The phonon dispersion curves of AmO2 are calculated and the heat capacities as well as lattice expansion curve are subsequently determined. The lattice thermal conductivity of AmO2 is further evaluated and compared with attainable experiments. Our present work integrally reveals various physical properties of AmO2 and can be referenced for technological applications of AmO2 based materials.
Lu, Yong; Yang, Yu; Zheng, Fawei; Wang, Bao-Tian; Zhang, Ping
1/n expansion in quantum mechanics
The classical approximation (/ell/ = n - 1 /yields/ /infinity/) for the energy /var epsilon/(/sup 0/) and the semiclassical expansion in problems of quantum mechanics are discussed. A recursive method is proposed for calculating the quantum corrections of arbitrary order to /var epsilon/ (/sup 0/), this being valid for both bound and quasistationary states. The generalization of the method to states with an arbitrary number of nodes and the possibility of a more general choice of the parameter of the semiclassical expansion are considered. The method is illustrated by the example of the Yukawa and funnel potentials and for the Stark effect in the hydrogen atom. These examples demonstrate the rapid convergence of the 1/n expansion even for small quantum numbers.
Vainberg, V.M.; Mur, V.D.; Popov, V.S.; Sergeev, A.V.; Shcheblykin, A.V.
Neutrino oscillations: Quantum mechanics vs. quantum field theory
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Akhmedov, Evgeny Kh.; Kopp, Joachim
Effects of quantum instantons on the thermodynamics of the CPN-1 model
NASA Astrophysics Data System (ADS)
Using the 1/N expansion, we study the influence of quantum instantons on the thermodynamics of the CPN-1 model in 1+1 dimensions. We do this by calculating the pressure to next-to-leading order in 1/N, without quantum instanton contributions. The fact that the CP1 model is equivalent to the O(3) nonlinear sigma model allows for a comparison to the full pressure up to 1/N2 corrections for N=3. Assuming validity of the 1/N expansion for the CP1 model makes it possible to argue that the pressure for intermediate temperatures is dominated by the effects of quantum instantons. A similar conclusion can be drawn for general N values by using the fact that the entropy should always be positive.
Andersen, Jens O.; Boer, Dani�l; Warringa, Harmen J.
Operational approach to fluctuations of thermodynamic variables in finite quantum systems
In this paper we present a quantum approach to the old problem of temperature fluctuations. We start by observing that according to quantum thermodynamics, fluctuations of intensive parameters like temperature cannot exist. Furthermore, such parameters are not observables, so their estimation has to be done indirectly. The respective temperature estimate based on quantum measurements of the energy is shown to fluctuate according to the well-known formula {Delta}T{sup 2}=(k{sub B}T{sup 2}/C), but only within a certain temperature range and if the system is not too small. We also calculate the fourth-order correction term, becoming important at higher temperatures. Finally we illustrate our results with a concrete model of n spins.
Jahnke, T.; Lanery, S.; Mahler, G. [Institut fuer Theoretische Physik 1, Universitaet Stuttgart, 70550 Stuttgart (Germany)
Fast method for quantum mechanical molecular dynamics
NASA Astrophysics Data System (ADS)
As the processing power available for scientific computing grows, first-principles Born-Oppenheimer molecular dynamics simulations are becoming increasingly popular for the study of a wide range of problems in materials science, chemistry, and biology. Nevertheless, the computational cost of Born-Oppenheimer molecular dynamics still remains prohibitively large for many potential applications. Here we show how to avoid a major computational bottleneck: the self-consistent-field optimization prior to force calculations. The optimization-free quantum mechanical molecular dynamics method gives trajectories that are almost indistinguishable from an �exact� microcanonical Born-Oppenheimer molecular dynamics simulation even when low-prefactor linear scaling sparse matrix algebra is used. Our findings show that the computational gap between classical and quantum mechanical molecular dynamics simulations can be significantly reduced.
Niklasson, Anders M. N.; Cawkwell, Marc J.
Applications of computational quantum mechanics
NASA Astrophysics Data System (ADS)
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts with novel properties. Doping a metal oxide may alter its intrinsic properties drastically. A catalytically non-active material can be activated by doping. In this study, we showed that pure zirconia (ZrO2) has almost no activity in methanol coupling reaction, whereas when it is doped with aluminum, the doped catalyst produces dimethyl ether (DME), which is valuable as an alternative future energy source.
Temel, Burcin
Collocation method for fractional quantum mechanics
We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on little sinc functions, which discretizes the Schroedinger equation on a uniform grid. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Good convergence properties are observed. A comparison with results based on a Wentzel-Kramers-Brillouin analysis is performed.
Amore, Paolo; Hofmann, Christoph P.; Saenz, Ricardo A. [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diagonal 113 y 64 S/N, Sucursal 4, Casilla de correo 16, 1900 La Plata (Argentina)
Grounding quantum probability in psychological mechanism.
Pothos & Busemeyer (P&B) provide a compelling case that quantum probability (QP) theory is a better match to human judgment than is classical probability (CP) theory. However, any theory (QP, CP, or other) phrased solely at the computational level runs the risk of being underconstrained. One suggestion is to ground QP accounts in mechanism, to leverage a wide range of process-level data. PMID:23673043
Love, Bradley C
Diffeomorphism groups and nonlinear quantum mechanics
NASA Astrophysics Data System (ADS)
This talk is dedicated to my friend and collaborator, Prof. Dr. Heinz-Dietrich Doebner, on the occasion of his 80th birthday. I shall review some highlights of the approach we have taken in deriving and interpreting an interesting class of nonlinear time-evolution equations for quantum-mechanical wave functions, with few equations; more detail may be found in the references. Then I shall comment on the corresponding hydrodynamical description.
Goldin, Gerald A.
Hunting for Snarks in Quantum Mechanics
NASA Astrophysics Data System (ADS)
A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function ? for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school (led by Bohr, Heisenberg and Pauli) holds that ? provides a complete description of a single electron state; hence the probability interpretation of ??* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school (led by Einstein, de Broglie, Bohm and Jaynes) holds that ? represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung (first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in ?. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark!
Hestenes, David
Relativistic non-Hermitian quantum mechanics
NASA Astrophysics Data System (ADS)
We develop relativistic wave equations in the framework of the new non-Hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that, in particular, the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here, we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but PT-symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is nonzero. The PT-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a noninteracting theory it violates P and T individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting possibilities permitted by the non-Hermiticity parameter m2.
Jones-Smith, Katherine; Mathur, Harsh
Hunting for Snarks in Quantum Mechanics
A long-standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger's wave function {psi} for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school(led by Bohr, Heisenberg and Pauli) holds that {psi} provides a complete description of a single electron state; hence the probability interpretation of {psi}{psi}* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school(led by Einstein, de Broglie, Bohm and Jaynes) holds that {psi} represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung(first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in {psi}. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark{exclamation_point}.
Hestenes, David [Physics Department, Arizona State University, Tempe, Arizona 85287 (United States)
Relativistic Statistical Thermodynamics
Bergmann has generalized Gibbs' classical statistical mechanics so as to make it applicable to both relativistic and quantum-mechanical systems. His method, however, involves some complicated differential geometry, and the resulting formulas are not easily manageable. A different method for obtaining a relativistic and quantized statistical thermodynamics is proposed which avoids the differential geometry and gives simpler final formulas. The end
A. E. Scheidegger; R. V. Krotkov
From Cbits to Qbits: Teaching computer scientists quantum mechanics
NASA Astrophysics Data System (ADS)
A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory. Although the article as a whole addresses teachers of physics well versed in quantum mechanics, the central pedagogical development is addressed directly to computer scientists and mathematicians, with only occasional asides to their teacher. Physicists uninterested in quantum pedagogy may be amused (or irritated) by some of the views of standard quantum mechanics that arise naturally from this unorthodox perspective.
Mermin, N. David
Theory of network contractor dynamics for exploring thermodynamic properties of two-dimensional quantum lattice models
NASA Astrophysics Data System (ADS)
Based on the tensor network state representation, we develop a nonlinear dynamic theory, coined network contractor dynamics (NCD), to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-1 decomposition in the multilinear algebra, the NCD scheme makes the contraction of the tensor network of the partition function be realized through a contraction of a local tensor cluster with vectors on its boundary. An imaginary-time-sweep algorithm for implementation of the NCD method is proposed for practical numerical simulations. We benchmark the NCD scheme on the square Ising model, which shows great accuracy. Also, the results on the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice are disclosed to be in good agreement with the quantum Monte Carlo calculations. The quasientanglement entropy S, Lyapunov exponent ILya, and loop character Iloop are introduced within the dynamic scheme, which are found to display �nonlocality� near the critical point, and can be applied to determine the thermodynamic phase transitions of both classical and quantum systems.
Ran, Shi-Ju; Xi, Bin; Liu, Tao; Su, Gang
Surveying Students' Understanding of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Development of research-based multiple-choice tests about quantum mechanics is important for assessing students' difficulties and for evaluating curricula and pedagogies that strive to reduce the difficulties. We explore the difficulties that the undergraduate and graduate students have with non-relativistic quantum mechanics of one particle in one spatial dimension. We developed a research-based conceptual multiple-choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, time-dependence of wavefunction and time-dependence of expectation value. We find that the advanced undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The survey can be administered to assess the effectiveness of various instructional strategies.
Singh, Chandralekha; Zhu, Guangtian
Surveying Students' Understanding of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Development of research-based multiple-choice tests about quantum mechanics is important for assessing students' difficulties and for evaluating curricula and pedagogies that strive to reduce the difficulties. We explore the difficulties that the undergraduate and graduate students have with non-relativistic quantum mechanics of one particle in one spatial dimension. We developed a research-based conceptual multiple-choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, time-dependence of wavefunction and time-dependence of expectation value. We find that the advanced undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The survey can be administered to assess the effectiveness of various intructional strategies.
Singh, Chandralekha; Zhu, Guangtian
Quantum mechanics with coordinate dependent noncommutativity
NASA Astrophysics Data System (ADS)
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
Kupriyanov, V. G.
Quantum mechanics with coordinate dependent noncommutativity
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
Kupriyanov, V. G. [CMCC, Universidade Federal do ABC, Santo Andr�, SP (Brazil)] [CMCC, Universidade Federal do ABC, Santo Andr�, SP (Brazil)
Topological quantum mechanics in 2 + 1 dimensions
The authors show that the classical and quantum covariant dynamics of spinning particles in flat space in 2 + 1 dimensions are derived from a pure Wess-Zumino term written on the space of adjoint orbits of the ISO(2,1) group. Similarly, the dynamics of spinning particles in 2 + 1 de Sitter (anti-de Sitter) space are derived from a Wess-Zumino term on the space of adjoint orbits of SO(3,1)(SO(2,2)). It is shown that a quantum mechanical description of spin is possible in 2 + 1 dimensions without introducing explicit spin degrees of freedom, but at the expense of having a noncommutative space-time geometry.
Skagerstam, B.S. (Inst. of Theoretical Physics, Chalmers Univ. of Technology, S-412 96 Goteborg (SE)); Stern, A. (Dept. of Physics and Astronomy, Univ. of Alabama, Tuscaloosa, AL (US))
Quantum Mechanics � la Langevin and Supersymmetry
NASA Astrophysics Data System (ADS)
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under ${\\mathcal N}=1$ SUSY, but can be obtained from a, manifestly, supersymmetric expression, upon fixing a local fermionic symmetry, called $\\kappa-$symmetry. The kinetic term for the fermions is a total derivative and can contribute only on the boundaries. We define combinations that scale appropriately, as the lattice spacing is taken to zero and the lattice size to infinity and provide evidence, by numerical simulations, that the correlation functions of the auxiliary field do satisfy Wick's theorem. We show, in particular, that simulations can be carried out using a purely bosonic action. The physical import is that the classical trajectory, $\\phi(\\tau)$, becomes a (chiral) superfield, $(\\phi(\\tau),\\psi_{\\alpha}(\\tau),F(\\tau))$, when quantum fluctuations are taken into account.
Nicolis, S.
Quantum mechanical Hamiltonian models of discrete processes
Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.
Benioff, P.
Thermodynamic limits for solar energy conversion by a quantum-thermal hybrid system
NASA Technical Reports Server (NTRS)
The limits are presented fo air mass 1.5 conditions. A maximum conversion efficiency of 74 percent is thermodynamically achievable for the quantum device operating at 3500 K and the heat engine in contact with a reservoir at 0 K. The efficiency drops to 56 percent for a cold reservoir at approximately room temperature conditions. Hybrid system efficiencies exceed 50 percent over receiver temperatures ranging from 1400 K to 4000 K, suggesting little benefit is gained in operating the system above 1400 K. The results are applied to a system consisting of a photovoltaic solar cell in series with a heat engine.
Byvik, C. E.; Buoncristiani, A. M.; Smith, B. T.
Thermodynamic properties of c-Si derived by quantum path-integral Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Feynman path-integral Monte Carlo simulations of crystalline silicon, using the empirical potential of Stillinger and Weber, have been performed in the isothermal-isobaric ensemble. Several thermodynamic properties have been evaluated as a function of pressure and temperature. The calculated lattice parameter, heat capacity, thermal expansion coefficient, and bulk modulus show an overall agreement with the experimental data. However, the negative thermal expansion of silicon at temperatures below 120 K is not reproduced with this model potential. The importance of anharmonicity and quantum effects on the properties derived from the Stillinger-Weber potential is addressed by comparison with the results expected in a quasiharmonic approximation and in the classical limit.
Noya, Jos� C.; Herrero, Carlos P.; Ram�rez, Rafael
Many-body quantum mechanics as a symplectic dynamical system
An approach is formulated to the problem of obtaining approximate solutions to many-body quantum mechanics. The starting point is the representation of quantum mechanics as Hamiltonian mechanics on a symplectic manifold (phase space). It is shown that Dirac's variation of an action integral provides a natural mechanism for constraining the dynamics to symplectic submanifolds and gives rise to a hierarchy
D. J. Rowe; A. Ryman; G. Rosensteel
The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics
NASA Astrophysics Data System (ADS)
We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation (SSE) with the Yukawa potential via the supersymmetric quantum mechanics (SUSYQM) for arbitrary quantum numbers. Useful figures and tables are also included.
Hassanabadi, S.; Ghominejad, M.; Zarrinkamar, S.; Hassanabadi, H.
Thermodynamic properties of the one-dimensional extended quantum compass model in the presence of a transverse field
NASA Astrophysics Data System (ADS)
The presence of a quantum critical point can significantly affect the thermodynamic properties of a material at finite temperatures. This is reflected, e.g., in the entropy landscape S(T, c) in the vicinity of a quantum critical point, yielding particularly strong variations for varying the tuning parameter c such as magnetic field. In this work we have studied the thermodynamic properties of the quantum compass model in the presence of a transverse field. The specific heat, entropy and cooling rate under an adiabatic demagnetization process have been calculated. During an adiabatic (de)magnetization process temperature drops in the vicinity of a field-induced zero-temperature quantum phase transitions. However close to field-induced quantum phase transitions we observe a large magnetocaloric effect.
Jafari, R.
Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions
NASA Astrophysics Data System (ADS)
We study the thermodynamics of the relativistic quantum O(N) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P(T)=P(0)+N(T3/c2)FN(?/T), where c is the velocity of the excitations at the QCP and |?| a characteristic zero-temperature energy scale. Using both a large-N approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function FN. For small values of N (N?10) we find that FN(x) is nonmonotonic in the quantum critical regime (|x|?1) with a maximum near x=0. The large-N approach�if properly interpreted�is a good approximation both in the renormalized classical (x?-1) and quantum disordered (x?1) regimes, but fails to describe the nonmonotonic behavior of FN in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio TBKT/?s(0) is very close to ?/2, implying that the stiffness ?s(TBKT-) at the transition is only slightly reduced with respect to the zero-temperature stiffness ?s(0). Finally, we briefly discuss the experimental determination of the universal function F2 from the pressure of a Bose gas in an optical lattice near the superfluid-Mott-insulator transition.
Ran�on, A.; Kodio, O.; Dupuis, N.; Lecheminant, P.
Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions.
We study the thermodynamics of the relativistic quantum O(N) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P(T)=P(0)+N(T(3)/c(2))F(N)(?/T), where c is the velocity of the excitations at the QCP and |?| a characteristic zero-temperature energy scale. Using both a large-N approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function F(N). For small values of N (N~10) we find that F(N)(x) is nonmonotonic in the quantum critical regime (|x|~1) with a maximum near x=0. The large-N approach-if properly interpreted-is a good approximation both in the renormalized classical (x~-1) and quantum disordered (x>/~1) regimes, but fails to describe the nonmonotonic behavior of F(N) in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio T(BKT)/?(s)(0) is very close to ?/2, implying that the stiffness ?(s)(T(BKT)(-)) at the transition is only slightly reduced with respect to the zero-temperature stiffness ?(s)(0). Finally, we briefly discuss the experimental determination of the universal function F(2) from the pressure of a Bose gas in an optical lattice near the superfluid-Mott-insulator transition. PMID:23944420
Ran�on, A; Kodio, O; Dupuis, N; Lecheminant, P
Quantum mechanics. Mechanically detecting and avoiding the quantum fluctuations of a microwave field.
Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 � 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 � 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion. PMID:24831528
Suh, J; Weinstein, A J; Lei, C U; Wollman, E E; Steinke, S K; Meystre, P; Clerk, A A; Schwab, K C
Testing Quantum Mechanics on New Ground
NASA Astrophysics Data System (ADS)
Preface; Acknowledgements; 1. Wave-particle duality; 2. Cavity quantum electrodynamics; 3. Quantum nondemolition measurements; 4. Topological phases; 5. Macroscopic quantum coherence; 6. The quantum Zeno paradox; 7. Testing collapse; 8. Macroscopic quantum jumps; 9. Nonlocality; 10. Tunneling times; References; Indexes.
Ghose, Partha
Scattering in PT-symmetric quantum mechanics
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with Hermiticity, T invariance and PT invariance.
Cannata, Francesco [Istituto Nazionale di Fisica Nucleare, Sezione di Bologna and Dipartimento di Fisica dell' Universita, Via Irnerio 46, I 40126 Bologna (Italy)]. E-mail: firstname.lastname@example.com; Dedonder, Jean-Pierre [GMPIB Universite Paris 7 - Denis-Diderot, 2 Place Jussieu, F-75251, Paris Cedex 05 (France)]. E-mail: email@example.com; Ventura, Alberto [Ente Nuove Tecnologie, Energia e Ambiente, Bologna and Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (Italy)]. E-mail: email@example.com
Improved lattice actions for supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
We analyze the Euclidean version of supersymmetric quantum mechanics on the lattice by means of a numerical path integral. We consider two different lattice derivatives and improve the actions containing them with respect to supersymmetry by systematically adding interaction terms with nonzero extent. To quantize this improvement, we measure boson and fermion masses and Ward identities for the naive as well as the improved models. The masses are degenerate in all models, but the magnitude of the Ward identities decreases significantly for both derivative operators using the improved actions. This is a clear sign that the breaking of supersymmetry due to lattice artifacts is reduced.
Schierenberg, Sebastian; Bruckmann, Falk
The metaphysics of quantum mechanics: Modal interpretations
NASA Astrophysics Data System (ADS)
This dissertation begins with the argument that a preferred way of doing metaphysics is through philosophy of physics. An understanding of quantum physics is vital to answering questions such as: What counts as an individual object in physical ontology? Is the universe fundamentally indeterministic? Are indiscernibles identical? This study explores how the various modal interpretations of quantum mechanics answer these sorts of questions; modal accounts are one of the two classes of interpretations along with so-called collapse accounts. This study suggests a new alternative within the class of modal views that yields a more plausible ontology, one in which the Principle of the Identity of Indisceribles is necessarily true. Next, it shows that modal interpretations can consistently deny that the universe must be fundamentally indeterministic so long as they accept certain other metaphysical commitments: either a perfect initial distribution of states in the universe or some form of primitive dispositional properties. Finally, the study sketches out a future research project for modal interpretations based on developing quantified quantum logic.
Gluck, Stuart Murray
Quantum Superspace, q-EXTENDED Supersymmetry and Parasupersymmetric Quantum Mechanics
NASA Astrophysics Data System (ADS)
We describe q-deformation of the extended supersymmetry and construct q-extended supersymmetric Hamiltonian. For this purpose we formulate q-superspace formalism and construct q-supertransformation group. On this basis q-extended supersymmetric Lagrangian is built. The canonical quantization of this system is considered. The connection with multi-dimensional matrix representations of the parasupersymmetric quantum mechanics is discussed and q-extended supersymmetric harmonic oscillator is considered as a simplest example of the described constructions. We show that extended supersymmetric Hamiltonians obey not only extended SUSY but also the whole family of symmetries (q-extended supersymmetry) which is parametrized by continuous parameter q on the unit circle.
Ilinski, K. N.; Uzdin, V. M.
Statistical mechanical expression of entropy production for an open quantum system
NASA Astrophysics Data System (ADS)
A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in quantum mechanics. The general relation between system-reservoir interactions and an entropy change operator in an open quantum system, relying just on the framework of statistical mechanics and the definition of von Neumann entropy. By using this formula, we can obtain the correct entropy production in the linear response framework. The present derivation of entropy production is directly based on the first principle of microscopic time-evolution, while the previous standard argument is due to the thermodynamic energy balance.
Majima, Hiroki; Suzuki, Akira
Comment on ``Arrival time in quantum mechanics'' and ``Time of arrival in quantum mechanics''
NASA Astrophysics Data System (ADS)
Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the ``time operator,'' which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.
Kijowski, Jerzy
Thermodynamic behavior of molecular-scale quantum-dot cellular automata (QCA) wires and logic devices
Quantum-dot cellular automata (QCA) offers a new paradigm for molecular electronics, a paradigm in which information transmission and processing depend on electrostatic interactions between charges in arrays of cells composed of quantum dots. Fundamental questions about the operational temperature and functional gain of devices built from molecular-scale QCA cells are addressed in this paper through a statistical-mechanical model based on
Yuliang Wang; Marya Lieberman
Nonlinear Riccati equations as a unifying link between linear quantum mechanics and other fields of physics
NASA Astrophysics Data System (ADS)
Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schr�dinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.
Schuch, Dieter
Noncommutative quantum mechanics as a gauge theory
The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second-class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system into an Abelian gauge theory exhibiting only first class constraints. The appropriateness of the BFT embedding, as implemented in this work, is verified by showing that there exists a one to one mapping linking the second-class model with the gauge invariant sector of the gauge theory. As is known, the functional quantization of a gauge theory calls for the elimination of its gauge freedom. Then, we have at our disposal an infinite set of alternative descriptions for noncommutative quantum mechanics, one for each gauge. We study the relevant features of this infinite set of correspondences. The functional quantization of the gauge theory is explicitly performed for two gauges and the results compared with that corresponding to the second-class system. Within the operator framework the gauge theory is quantized by using Dirac's method.
Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, RS (Brazil)
The formal path integral and quantum mechanics
Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
Johnson-Freyd, Theo [Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Berkeley, California 94720 (United States)
BOOK REVIEW: Mind, Matter and Quantum Mechanics (2nd edition)
Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried
H. P. Stapp
Mind, Matter and Quantum Mechanics (2nd edition)
Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried
G Mahler
Probability in the formalism of quantum mechanics on phase space
NASA Astrophysics Data System (ADS)
The methods of Born and Einstein are used to obtain the probability density in the formalism of quantum mechanics on phase space. The resulting probability leads to a contextual measurement scheme. The Wigner representation, the Husimi representation and the mass shell representation are discussed from the point of view of quantum mechanics on phase space. We also give ramifications for paradoxes in standard quantum mechanics.
Schroeck, Franklin E., Jr.
Synthesis mechanism of lithium nickel oxide using hydrothermal electrochemical method: Thermodynamic modelling and experimental verification
NASA Astrophysics Data System (ADS)
Potential-pOH diagrams of nickel are drawn at various temperatures to predict the reaction of nickel in a 4 M lithium hydroxide solution. Based on these diagrams, the thermodynamic stability of each constituent of nickel in 4 M LiOH solution at various temperatures is evaluated. The oxidation mechanism is studied based on the thermodynamic analysis and the oxidation proceeds in the following order: Ni, Ni(OH) 2 or HNiO 2-, NiOOH rad H 2O, NiOOH, LiNiO 2. The thermodynamic model is validated experimentally by the cyclic voltammogram method.
Tao, Ying; Chen, Zhenhua; Zhu, Baojun
A Quantum Mechanics\\/Molecular Mechanics Study of the Catalytic Mechanism of the Thymidylate Synthase �
A theoretical study of the molecular mechanism of the thymidylate synthase-catalyzed reaction has been carried out using hybrid quantum mechanics\\/molecular mechanics methods. We have examined all of the stationary points (reactants, intermediates, transition structures, and products) on the multidimensional potential energy surfaces for the multistep enzymatic process. The characterization of these relevant structures facilitates the gaining of insight into the
Natalia Kanaan; Sergio Mart�; Vicent Moliner; Amnon Kohen
Relationship between quantum-mechanical systems with and without monopoles
It is shown that the inclusion of the monopole field in the three- and five-dimensional spherically symmetric quantum-mechanical systems, with the addition of the special centrifugal term, leads to the lift of the range of the total and azimuth quantum numbers only. Meanwhile the functional dependence of the energy spectra on quantum numbers does not undergo any changes. We also
Levon Mardoyan; Armen Nersessian; Armen Yeranyan
Induced representations of quantum kinematical algebras and quantum mechanics
NASA Astrophysics Data System (ADS)
Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. In this paper we propose their generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper (Arratia O and del Olmo M A 2001 Preprint math.QA/0110275) to induce representations of quantum bicrossproduct algebras, we construct the representations of the family of standard quantum inhomogeneous algebras U?(iso?(2)). This family contains the quantum Euclidean, Galilei and Poincar� algebras, all of them in (1+1) dimensions. As byproducts we obtain the actions of these quantum algebras on regular co-spaces that are an algebraic generalization of the homogeneous spaces and q-Casimir equations which play the role of q-Schr�dinger equations.
Arratia, Oscar; del Olmo, Mariano A.
Quantum Mechanics with Basic Field Theory
NASA Astrophysics Data System (ADS)
Preface; 1. Basic formalism; 2. Fundamental commutator and time evolution of state vectors and operators; 3. Dynamical equations; 4. Free particles; 5. Particles with spin 1/2; 6. Gauge invariance, angular momentum and spin; 7. Stern-Gerlach experiments; 8. Some exactly solvable bound state problems; 9. Harmonic oscillator; 10. Coherent states; 11. Two-dimensional isotropic harmonic oscillator; 12. Landau levels and quantum Hall effect; 13. Two-level problems; 14. Spin 1/2 systems in the presence of magnetic field; 15. Oscillation and regeneration in neutrino and neutral K-mesons as two-level systems; 16. Time-independent perturbation for bound states; 17. Time-dependent perturbation; 18. Interaction of charged particles and radiation in perturbation theory; 19. Scattering in one dimension; 20. Scattering in three dimensions - a formal theory; 21. Partial wave amplitudes and phase shifts; 22. Analytic structure of the S-matrix; 23. Poles of the Green's function and composite systems; 24. Approximation methods for bound states and scattering; 25. Lagrangian method and Feynman path integrals; 26. Rotations and angular momentum; 27. Symmetry in quantum mechanics and symmetry groups; 28. Addition of angular momenta; 29. Irreducible tensors and Wigner-Eckart theorem; 30. Entangled states; 31. Special theory of relativity: Klein Gordon and Maxwell's equation; 32. Klein Gordon and Maxwell's equation; 33. Dirac equation; 34. Dirac equation in the presence of spherically symmetric potentials; 35. Dirac equation in a relativistically invariant form; 36. Interaction of Dirac particle with electromagnetic field; 37. Multiparticle systems and second quantization; 38. Interactions of electrons and phonons in condensed matter; 39. Superconductivity; 40. Bose Einstein condensation and superfluidity; 41. Lagrangian formulation of classical fields; 42. Spontaneous symmetry breaking; 43. Basic quantum electrodynamics and Feynman diagrams; 44. Radiative corrections; 45. Anomalous magnetic moment and Lamb shift; Appendix; References; Index.
Desai, Bipin R.
a Quantum Mechanical Semiconductor Device Simulator.
NASA Astrophysics Data System (ADS)
Semiconductor device simulators have generally been based on either classical or semi-classical approaches. In these approaches, the Poisson's equation is solved with either the current continuity equation or the Boltzmann transport equation. Methods based on quantum mechanics have been generally very computer intensive, and thus until recently not much favored. However, with the availability of faster and more powerful computers this picture is changing. As the physical dimensions of the semiconductor devices are reduced, the assumptions made in the classical and the semi-classical approaches become invalid and the simulation results become inaccurate. For such cases, quantum mechanical concepts must be introduced to provide accurate simulation results. This dissertation presents the proof of concept of a semiconductor device simulator based on the quantum mechanical principals. The simulation technique is based on the self consistent solution of the Poisson's and time independent Schrodinger wave equation for a 1-D finite differenced grid. The applicability of the technique to a 2-D finite differenced grid is also presented. The simulation is performed by first solving for the Fermi energy distribution inside the simulation domain. The initial estimates about the carrier concentrations are developed from the Fermi energy distribution. Based on the carrier concentrations, the potential distribution inside the device is updated using the Poisson's equation. The updated potential distribution is then used in the time independent Schrodinger's equation and the carrier wave vectors are thus determined. The carrier wave vectors, along with appropriate density of state function and distribution function are used to update the carrier concentrations. For the 1-D case, the density of state function is based on a single dimension of a three dimensional volume with the assumption that the density of states is the same for all the three dimensions. The distribution function used is the Fermi-Dirac distribution function. The new carrier concentrations thus computed are then substituted back into the Poisson's equation, and self consistency is obtained when minimum error criteria have been met. The device simulator has the capability of simulating heterojunctions semiconductor devices fabricated from elemental semiconductors such as Si and Ge, as well as binary and tertiary compound semiconductors.
Bhutta, Imran Ahmed
Tampering detection system using quantum-mechanical systems
The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.
Humble, Travis S. (Knoxville, TN); Bennink, Ryan S. (Knoxville, TN); Grice, Warren P. (Oak Ridge, TN)
Thermodynamics of liquid metal
The thermodynamics of a liquid metal based on quantum-mechanical models of the crystal, electronic, and nuclear structures of the metal are derived in this paper. The models are based on such formulations as the Bohr radius, the Boltzmann constant, the Planck Law, the Fermi surface, and the Pauli principle.
Kushnirenko, A.N.
Moyal quantum mechanics: The semiclassical Heisenberg dynamics
The Moyal description of quantum mechanics, based on the Wigner--Weyl isomorphism between operators and symbols, provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in {h_bar} and so presents a preferred foundation for semiclassical analysis. Its semiclassical expansion ``coefficients,`` acting on symbols that represent observables, are simple, globally defined (phase space) differential operators constructed in terms of the classical flow. The first of two presented methods introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold`s formula for the Weyl product of two symbols and has {h_bar} as its natural small parameter. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of ``quantum trajectories.`` Their Green function solutions construct the regular {h_bar}{down_arrow}0 asymptotic series for the Heisenberg--Weyl evolution map. The second method directly substitutes such a series into the Moyal equation of motion and determines the {h_bar} coefficients recursively. In contrast to the WKB approximation for propagators, the Heisenberg--Weyl description of evolution involves no essential singularity in {h_bar}, no Hamilton--Jacobi equation to solve for the action, and no multiple trajectories, caustics, or Maslov indices. {copyright} 1995 Academic Press, Inc.
Osborn, T.A.; Molzahn, F.H. [Department of Physics, University of Manitoba, Winnipeg, MB, R3T 2N2 (Canada)] [Department of Physics, University of Manitoba, Winnipeg, MB, R3T 2N2 (Canada)
Quantum four-stroke heat engine: thermodynamic observables in a model with intrinsic friction.
The fundamentals of a quantum heat engine are derived from first principles. The study is based on the equation of motion of a minimum set of operators, which is then used to define the state of the system. The relation between the quantum framework and the thermodynamical observables is examined. A four-stroke heat engine model with a coupled two-level system as a working fluid is used to explore the fundamental relations. In the model used, the internal Hamiltonian does not commute with the external control field, which defines the two adiabatic branches. Heat is transferred to the working fluid by coupling to hot and cold reservoirs under constant field values. Explicit quantum equations of motion for the relevant observables are derived on all branches. The dynamics on the heat transfer constant field branches is solved in closed form. On the adiabats, a general numerical solution is used and compared with a particular analytic solution. These solutions are combined to construct the cycle of operation. The engine is then analyzed in terms of the frequency-entropy and entropy-temperature graphs. The irreversible nature of the engine is the result of finite heat transfer rates and frictionlike behavior due to noncommutability of the internal and external Hamiltonians. PMID:12935194
Feldmann, Tova; Kosloff, Ronnie
Quantum mechanics without an equation of motion
We propose a formulation of quantum mechanics for a finite level system whose potential function is not realizable and/or analytic solution of the wave equation is not feasible. The system's wavefunction is written as an infinite sum in a complete set of square integrable functions. Interaction in the theory is introduced in function space by a real finite tridiagonal symmetric matrix. The expansion coefficients of the wavefunction satisfy a three-term recursion relation incorporating the parameters of the interaction. Information about the structure and dynamics of the system is contained in the scattering matrix, which is defined in the usual way. The bound state energy spectrum (system's structure) is finite. Apart from the 2M- 1 dimensionless parameters of the interaction matrix, whose rank is M, the theory has one additional scale parameter. In the development, we utilize the kinematic tools of the J-matrix method.
Alhaidari, A. D. [Saudi Center for Theoretical Physics, Jeddah 21438 (Saudi Arabia)
Supersymmetric quantum mechanics and Painlev� equations
NASA Astrophysics Data System (ADS)
In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlev� IV (PIV) and Painlev� V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.
Bermudez, David; Fern�ndez C., David J.
Nonlinear supersymmetric quantum mechanics: concepts and realizations
NASA Astrophysics Data System (ADS)
The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described. It is elaborated how the nonlinear SUSY approach provides two new methods of SUSY separation of variables for various two-dimensional models. In the framework of these methods, a partial and/or complete solution of some two-dimensional models becomes possible. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. The emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of the nonlinear SUSY in one-dimensional stationary and non-stationary, as well as in two-dimensional QM.
Andrianov, A. A.; Ioffe, M. V.
Twist deformations of the supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
The mathcal{N} -extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even mathcal{N} one can identify the 1 D mathcal{N} -extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.
Castro, Paulo G.; Chakraborty, Biswajit; Kuznetsova, Zhanna; Toppan, Francesco
Twist deformation of rotationally invariant quantum mechanics
Noncommutative quantum mechanics in 3D is investigated in the framework of an abelian Drinfeld twist which deforms a given Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential), and the Coulomb potential.
Chakraborty, B. [S.N. Bose National Center for Basic Sciences, JD Block, Sector III, Salt-Lake, Kolkata-700098 (India); Kuznetsova, Z. [UFABC, Rua Catequese 242, Bairro Jardim, cep 09090-400, Santo Andre (Brazil); Toppan, F. [CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (Brazil)
Relativistic quantum mechanics of supersymmetric particles
NASA Astrophysics Data System (ADS)
The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge supersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one indludes in the action the boundary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix.
Henneaux, Marc; Teitelboim, Claudio
Relativistic quantum mechanics of supersymmetric particles
The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge sypersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one includes in the action the bounary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix.
Henneaux, M.; Teitelboim, C.
New methods for quantum mechanical reaction dynamics
Quantum mechanical methods are developed to describe the dynamics of bimolecular chemical reactions. We focus on developing approaches for directly calculating the desired quantity of interest. Methods for the calculation of single matrix elements of the scattering matrix (S-matrix) and initial state-selected reaction probabilities are presented. This is accomplished by the use of absorbing boundary conditions (ABC) to obtain a localized (L{sup 2}) representation of the outgoing wave scattering Green`s function. This approach enables the efficient calculation of only a single column of the S-matrix with a proportionate savings in effort over the calculation of the entire S-matrix. Applying this method to the calculation of the initial (or final) state-selected reaction probability, a more averaged quantity, requires even less effort than the state-to-state S-matrix elements. It is shown how the same representation of the Green`s function can be effectively applied to the calculation of negative ion photodetachment intensities. Photodetachment spectroscopy of the anion ABC{sup -} can be a very useful method for obtaining detailed information about the neutral ABC potential energy surface, particularly if the ABC{sup -} geometry is similar to the transition state of the neutral ABC. Total and arrangement-selected photodetachment spectra are calculated for the H{sub 3}O{sup -} system, providing information about the potential energy surface for the OH + H{sub 2} reaction when compared with experimental results. Finally, we present methods for the direct calculation of the thermal rate constant from the flux-position and flux-flux correlation functions. The spirit of transition state theory is invoked by concentrating on the short time dynamics in the area around the transition state that determine reactivity. These methods are made efficient by evaluating the required quantum mechanical trace in the basis of eigenstates of the Boltzmannized flux operator.
Thompson, W.H. [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry]|[Lawrence Berkeley Lab., CA (United States)
Mechanism and thermodynamics of ligand binding to auxin amidohydrolase.
BrILL2 is catalytically the most efficient auxin amidohydrolase from Brassica rapa, playing a key role in auxin metabolism by catalyzing its release from amino acid conjugates. Auxins, with the most abundant representative indole-acetic acid ([1H-indol-3-yl]-acetic acid, IAA), are a group of plant hormones that in very small concentrations regulate ubiquitin-mediated degradation of transcription regulators. Kinetic studies on BrILL2 showed that it hydrolyzes alanine conjugates of IAA and of its larger analogues, indole-propionic acid (3-[1H-indol-3-yl]-propionic acid, IPA) and indole-butyric acid (4-[1H-indol-3-yl]-butyric acid, IBA). Structurally, BrILL2 belongs to the largest known family of metallopeptidases (M20) that share a recognizable 3D structure, characterized by two perpendicular domains. Its members have been implicated in numerous biochemical processes and have been found across all species sequenced to date. Here, molecular dynamics simulations were carried out to study structural and thermodynamic properties of ligand binding to BrILL2. A conformational change was captured in multiple copies of 10?ns long simulations, described by a rigid body movement of the two domains, and its associated key interactions between residues were examined. For the three substrates, complexes in two possible binding modes were recreated, along with a single binding mode for the putative substrate tryptophanyl-alanine (Trp-Ala), which were subsequently simulated in multiple copies of 10?ns long simulations. Thermodynamic calculations were used to assess their binding affinities and explain the selectivity toward the longer ligands. Based on the results, a possible route for the reaction is proposed. PMID:21812060
Simunovic, Mijo; Zagrovic, Bojan; Tomi?, Sanja
Interactive Quantum Mechanics Exercises for Just-in-Time Teaching
NSDL National Science Digital Library
This is a collection of online curricular material for a one-semester quantum mechanics course. It consists of interactive Java applets, Physlets, for interactive out-of-class exercises. These applets stress the visualization of quantum mechanical concepts for better student understanding. There are also illustrations suitable for both in-class and out-of-class use.
Belloni, Mario; Cain, Laurence; Christian, Wolfgang
Rigorous solution to a quantum statistical mechanical laser model
A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal
Fumiaki Shibata; Chikako Uchiyama
Inner-Shell Physics after Fifty Years of Quantum Mechanics.
National Technical Information Service (NTIS)
A historical view is given of how the development of quantum mechanics has been affected by the information relating to inner shells, gathered by physicists since the early days of atomic physics, and of the impact of quantum mechanics on the physics of i...
E. Merzbacher
On the End of a Quantum Mechanical Romance
Comparatively recent advances in quantum measurement theory suggest that the decades-old flirtation between quantum mechanics and the philosophy of mind is about to end. Various approaches to what I have elsewhere dubbed 'interactive decoherence' promise to remove the conscious observer from the phenomenon of state vector reduction. The mechanisms whereby decoherence occurs suggest, on the one hand, that consciousness per
Gregory R. Mulhauser
The Quantum and Fluid Mechanics of Global Warming
Quantum physics and fluid mechanics are the foundation of any understanding of the Earth's climate. In this talk I invoke three well-known aspects of quantum mechanics to explore what will happen as the concentrations of greenhouse gases such as carbon dioxide continue to increase. Fluid dynamical models of the Earth's atmosphere, demonstrated here in live simulations, yield further insight into
Brad Marston
Effect of violation of quantum mechanics on neutrino oscillation
NASA Astrophysics Data System (ADS)
The effect of quantum mechanics violation due to quantum gravity on neutrino oscillation is investigated. It is found that the mechanism introduced by Ellis, Hagelin, Nanopoulos, and Srednicki through the modification of the Liouville equation can affect neutrino oscillation behavior and may be taken as a new solution of the solar neutrino problem.
Liu, Yong; Hu, Liangzhong; Ge, Mo-Lin
Linear Logic for Generalized Quantum Mechanics
Quantum logic is static, describing automata having uncertain states but no state transitions and no Heisenberg uncertainty tradeo. We cast Girard's linear logic in the role of a dynamic quantum logic, regarded as an extension of quantum logic with time nonstandardly interpreted over a domain of linear automata and their dual linear schedules. In this extension the uncertainty tradeo emerges
Vaughan Pratt
Lectures on Black Hole Quantum Mechanics
NASA Astrophysics Data System (ADS)
The lectures that follow were originally given in 1992, and written up only slightly later. Since then there have been dramatic developments in the quantum theory of black holes, especially in the context of string theory. None of these are reflected here. The concept of quantum hair, which is discussed at length in the lectures, is certainly of permanent interest, and I continue to believe that in some generalized form it will prove central to the whole question of how information is stored in black holes. The discussion of scattering and emission modes from various classes of black holes could be substantially simplified using modern techniques, and from currently popular perspectives the choice of examples might look eccentric. On the other hand fashions have changed rapidly in the field, and the big questions as stated and addressed here, especially as formulated for "real" black holes (nonextremal, in four-dimensional, asymptotically flat space-time, with supersymmetry broken), remain pertinent even as the tools to address them may evolve. The four lectures I gave at the school were based on two lengthy papers that have now been published, "Black Holes as Elementary Particles," Nuclear Physics B380, 447 (1992) and "Quantum Hair on Black Holes," Nuclear Physics B378, 175 (1992). The unifying theme of this work is to help make plausible the possibility that black holes, although they are certainly unusual and extreme states of matter, may be susceptible to a description using concepts that are not fundamentally different from those we use in describing other sorts of quantum-mechanical matter. In the first two lectures I discussed dilaton black holes. The fact that apparently innocuous changes in the "matter" action can drastically change the properties of a black hole is already very significant: it indicates that the physical properties of small black holes cannot be discussed reliably in the abstract, but must be considered with due regard to the rest of physics. (The macroscopic properties of large black holes, in particular those of astrophysical interest, are presumably well described by the familiar Einstein-Maxwell action which governs the massless fields. Heavy fields will at most provide Yukawa tails to the field surrounding the hole.) I will show how perturbations may be set up and analyzed completely, and why doing this is crucial for understanding the semiclassical physics of the hole including the Hawking radiation quantitatively. It will emerge that there is a class of dilaton black holes which behave as rather straightforward elementary particles. In the other two lectures I discussed the issue of hair on black holes, in particular the existence of hair associated with discrete gauge charges and its physical consequences. This hair is particularly interesting to analyze because it is invisible classically and to all order in ?. Its existence shows that black holes can have some "internal" quantum numbers in addition to their traditional classification by mass, charge, and angular momentum. The text that follows, follows the original papers closely.
Wilczek, Frank
Quantum mechanics/molecular mechanics study of oxygen binding in hemocyanin.
We report a combined quantum mechanics/molecular mechanics (QM/MM) study on the mechanism of reversible dioxygen binding in the active site of hemocyanin (Hc). The QM region is treated by broken-symmetry density functional theory (DFT) with spin projection corrections. The X-ray structures of deoxygenated (deoxyHc) and oxygenated (oxyHc) hemocyanin are well reproduced by QM/MM geometry optimizations. The computed relative energies strongly depend on the chosen density functional. They are consistent with the available thermodynamic data for oxygen binding in hemocyanin and in synthetic model complexes when the BH&HLYP hybrid functional with 50% Hartree-Fock exchange is used. According to the QM(BH&HLYP)/MM results, the reaction proceeds stepwise with two sequential electron transfer (ET) processes in the triplet state followed by an intersystem crossing to the singlet product. The first ET step leads to a nonbridged superoxo CuB(II)-O2(�-) intermediate via a low-barrier transition state. The second ET step is even more facile and yields a side-on oxyHc complex with the characteristic Cu2O2 butterfly core, accompanied by triplet-singlet intersystem crossing. The computed barriers are very small so that the two ET processes are expected to very rapid and nearly simultaneous. PMID:24762083
Saito, Toru; Thiel, Walter
Mechanics and thermodynamics of propulsion (2nd revised and enlarged edition)
NASA Astrophysics Data System (ADS)
The present volume proceeds under the principle that a few fundamental physical principles can with suitable application furnish students of mechanical and aeronautical engineering with an understanding of all aspects of aircraft and spacecraft propulsion. This methodology can further yield usefully quantitative assessments of performance, and indicate prospects for further improvement. Attention is given to the jet propulsion principle, the mechanics and thermodynamics of fluid flow, the thermodynamics of aircraft gas turbine engines, axial compressors and turbines, centrifugal compressors, chemical propellant rocket engine operation and performance, turbomachinery for liquid propellant rockets, and electrical rocket propulsion.
Hill, Philip G.; Peterson, Carl R.
Mechanics, thermodynamics and locomotive design: The machine?ensemble and the development of industrial thermodynamics
The need to treat history of technology as history of ideas is stressed and a definition of philosophy by G.C. Lichtenberg is adapted to serve as a tool for analysing technological change.A case study of locomotive design is introduced, and the influence of rational mechanics, on the machine?ensemble or locomotive?track union, beginning with the work. of L. Carnot, is briefly
M. C. Duffy
Mechanics of quantum and Sharvin conductors
NASA Astrophysics Data System (ADS)
Previously, the authors reported direct evidence of channel saturation and conductance quantization in atomic-sized gold constrictions through mechanical perturbation studies, and also showed that peaks in conductance histograms are insufficient in evaluating their mechanical stability [Armstrong , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.82.195416 82, 195416 (2010)]. In the present study, gold constrictions spanning the range from quantum to semiclassical (Sharvin) conductance regimes are mechanically probed with picolevel resolution in applied force and deformation, along with simultaneous measurements of conductance. While reconfiguration from one constriction size to another is known to occur by apparently random discrete atomic displacements, results reveal a remarkable simplicity�the magnitude of discrete atomic displacements is limited to a small set of values that correspond to elementary slip distances in gold rather than Au-Au interatomic distance. Combined with measurements of the spring constant of constrictions, results reveal two fundamental crossovers in deformation modes with increasing contact diameter�first, from homogeneous shear to defect-mediated deformation at a diameter that is in close agreement with previous predictions [S�rensen , Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.57.3283 57, 3283 (1998)]; and second, the discovery of another crossover marking surface- to volume-dominated deformation. A remarkable modulus enhancement is observed when the size of the constrictions approaches the Fermi wavelength of the electrons, and in the limit of a single-atom constriction it is at least two times that for bulk gold. Results provide atomistic insight into the stability of these constrictions and an evolutionary trace of deformation modes, beginning with a single-atom contact.
Armstrong, Jason N.; Hua, Susan Z.; Chopra, Harsh Deep
Mechanisms of antimicrobial, cytolytic, and cell-penetrating peptides: from kinetics to thermodynamics�
The mechanisms of six different antimicrobial, cytolytic, and cell-penetrating peptides, including some of their variants, are discussed and compared. The specificity of these polypeptides varies, but they all form amphipathic ?-helices when bound to membranes, and there are no striking differences in their sequences. We have examined the thermodynamics and kinetics of their interaction with phospholipid vesicles, namely binding and peptide-induced dye efflux. The thermodynamics of binding calculated using the Wimley-White interfacial hydrophobicity scale are in good agreement with the values derived from experiment. The generally accepted view that binding affinity determines functional specificity is also supported by experiment in model membranes. We now propose the hypothesis that it is the thermodynamics of peptide insertion into the membrane, from a surface-bound state, that determines the mechanism.
Almeida, Paulo F.; Pokorny, Antje
On physical and mathematical causality in quantum mechanics
NASA Astrophysics Data System (ADS)
This paper critically examines the view of quantum phenomena that has persisted since the introduction of quantum mechanics and that still remains prevalent in the foundational literature on quantum theory. According to this view, the independent behavior of quantum systems is causal, while the experimentally manifest lack of causality in observable quantum phenomena and, as a result, the probabilistic nature of our predictions concerning these phenomena are due to the disruption of this causal behavior by interfering with it through the measuring process. It appears that this view originates with P. A. M. Dirac and his work on the transformation theory (introduced by him and P. Jordan), which brought together W. Heisenberg's and E. Schr�dinger's versions of quantum mechanics within a single scheme. Other founding figures of quantum theory, specifically N. Bohr, W. Heisenberg, and J. von Neumann, also advanced this view and helped to establish its prominence. The paper discusses these arguments and contends them to be insufficient to support the view that the independent behavior quantum systems is physically causal. It suggests that one can meaningfully speak of mathematical causality in quantum theory, and advocates an alternative, physically noncausal, interpretation of quantum mechanics.
Plotnitsky, Arkady
Water properties from first principles: Simulations by a general-purpose quantum mechanical polarizable force field
We have recently introduced a quantum mechanical polarizable force field (QMPFF) fitted solely to high-level quantum mechanical data for simulations of biomolecular systems. Here, we present an improved form of the force field, QMPFF2, and apply it to simulations of liquid water. The results of the simulations show excellent agreement with a variety of experimental thermodynamic and structural data, as good or better than that provided by specialized water potentials. In particular, QMPFF2 is the only ab initio force field to accurately reproduce the anomalous temperature dependence of water density to our knowledge. The ability of the same force field to successfully simulate the properties of both organic molecules and water suggests it will be useful for simulations of proteins and protein�ligand interactions in the aqueous environment.
Donchev, A. G.; Galkin, N. G.; Illarionov, A. A.; Khoruzhii, O. V.; Olevanov, M. A.; Ozrin, V. D.; Subbotin, M. V.; Tarasov, V. I.
Water properties from first principles: simulations by a general-purpose quantum mechanical polarizable force field.
We have recently introduced a quantum mechanical polarizable force field (QMPFF) fitted solely to high-level quantum mechanical data for simulations of biomolecular systems. Here, we present an improved form of the force field, QMPFF2, and apply it to simulations of liquid water. The results of the simulations show excellent agreement with a variety of experimental thermodynamic and structural data, as good or better than that provided by specialized water potentials. In particular, QMPFF2 is the only ab initio force field to accurately reproduce the anomalous temperature dependence of water density to our knowledge. The ability of the same force field to successfully simulate the properties of both organic molecules and water suggests it will be useful for simulations of proteins and protein-ligand interactions in the aqueous environment. PMID:16723394
Donchev, A G; Galkin, N G; Illarionov, A A; Khoruzhii, O V; Olevanov, M A; Ozrin, V D; Subbotin, M V; Tarasov, V I
Interaction effects in the thermodynamic properties of quantum-dots: a Hartree-Fock study.
NASA Astrophysics Data System (ADS)
We study electron-electron interaction effects in the thermodynamic properties of quantum-dot systems. Using a finite-temperature self-consistent Hartree-Fock method, [1,2,3] we obtain the direct and exchange contributions to the specific heat Cv of square quantum dots of size L with up to N=20 electrons. An exchange-induced phase transition [2] is observed at a finite transition temperature T^*. Our analysis shows that T^* scales with L-1 and is on the range of a few Kelvin for dots tens of nanometers across. The exchange contribution to Cv dominates over the direct and kinetic contributions in the intermediate regime of interaction strength (rs�1), similarly to results obtained for the magnetic susceptibility [3]. Furthermore, the specific oscillates as function of an applied magnetic field and both oscillation amplitude and period are modified by the electron-electron interaction. Supported by FAPESP-Brazil. [1] H. Tamura and M. Ueda, Phys. Rev. Lett. 79 1345 (1997). [2] D. J. Dean, M. R. Strayer, and J. C. Wells, Phys. Rev. B 64, 125305 (2001). [3] L. G. G. V. Dias da Silva, C. Lewenkopf, and Nelson Studart, Phys. Rev. B 69, 075311 (2004).
Studart, Nelson; Dias da Silva, Luis
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation
NASA Astrophysics Data System (ADS)
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
Resources Students Use to Understand Quantum Mechanical Operators
NSDL National Science Digital Library
The Paradigms team at Oregon State University has developed a quantum mechanics curriculum aimed at middle division students that begins with a strong emphasis on using operators, matrices and Dirac notation to describe quantum systems. The curriculum begins with spin systems, and this content ordering relies on students being able to understand quantum mechanical operators, eigenstates and quantum measurement without prior instruction on wave functions. We have analyzed classroom and an interview video to identify resources students use when considering these quantum ideas. Identification of such resources will inform introductory curricula that are prerequisite to the quantum Paradigms and inform the development of Paradigms materials that will guide students to use these resources productively.
Gire, Elizabeth; Manogue, Corinne A.
Thermodynamics and nonlinear mechanics of materials with photoresponsive microstructure
NASA Astrophysics Data System (ADS)
The ability to directly convert visible light radiation into useful mechanical work provides many opportunities in the field of smart materials and adaptive structures ranging from biomedical applications to control of heliostat mirrors for solar harvesting. The complexities associated with coupling time-dependent Maxwell's equations with linear momentum and mechanics is discussed by introducing a set of electronic order parameters that govern the coupling between electromagnetic radiation and mechanics of a deformable solid. Numerical examples are given illustrating how this methodology is applied to a special class of liquid crystal polymer networks containing azobenzene. The dynamics associated with light absorption and its effect on deformation of the polymer are solved in three dimensions using finite difference methods and compared to experimental results. Particular emphasis is placed on the effect of polarized light on microstructure evolution and stresses that occur during photoisomerization of the optically active microstructure.
Oates, William S.; Bin, Jonghoon
Quantum mechanical model for Maya Blue
NASA Astrophysics Data System (ADS)
This work is about Maya Blue (MB), a pigment developed by Mesoamerican civilizations between the 5th and 16th centuries from an aluminosilicate mineral (palygorskite) and an organic dye (indigo). Two different supramolecular quantum-mechanical models afford explanations for the unusual stability of MB based on the oxidation of the indigo molecule during the heating process and its interaction with palygorskite. A model considering indigo derivatives attached to several aluminates shows the principal features of the experimental visible spectrum of MB within the TD-DFT methodology. Another model of an indigo oxidized species confined within an inorganic supramolecular cavity system, that involves about 170 atoms, was calculated after a large configuration interaction of single excited determinants within the NDOL approximation (Montero-Cabrera et al., J Chem Phys, 2007, 127, 145102). It allows a correct reproduction and interpretation of the corresponding spectrum. This second methodology provides the most satisfactory results, being able to manage very big molecular systems at a QM level. Structural explanation for the unusual stability of MB is also provided.
Fuentes, Mar�a E.; Pe�a, Brisa; Contreras, C�sar; Montero, Ana L.; Chianelli, Russell; Alvarado, Manuel; Olivas, Ram�n; Rodr�guez, Luz M.; Camacho, H�ctor; Montero-Cabrera, Luis A.
Quantum Mechanical Studies of DNA and LNA
Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the electrostatic potentials were compared among model oligonucleotides, and it was observed that small structural modifications induce global changes in the molecular structure and surface potentials. Since ligand structure and electrostatic potential complementarity with a receptor is a determinant for the bonding pattern between molecules, minor chemical modifications may have profound changes in the interaction profiles of oligonucleotides, possibly leading to changes in pharmacological properties. The QM modeling data can be used to understand earlier observations of antisense oligonucleotide properties, that is, the observation that small structural changes in oligonucleotide composition may lead to dramatic shifts in phenotypes. These observations should be taken into account in future oligonucleotide drug discovery, and by focusing more on non RNA target interactions it should be possible to utilize the exhibited property diversity of oligonucleotides to produce improved antisense drugs.
Shim, Irene; Lindow, Morten; ?rum, Henrik
Development and validation of an achievement test in introductory quantum mechanics: The Quantum Mechanics Visualization Instrument (QMVI)
NASA Astrophysics Data System (ADS)
The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p < 0.05). That finding is consistent with the additional understanding and experience that should be anticipated in graduate students and junior-senior level students over sophomore physics majors and majors in another field. The moderate positive correlation coefficient of 0.42 observed between students' QMVI scores and their final course grades was also consistent with expectations in a valid instrument. In addition, the Cronbach-alpha reliability coefficient of the QMVI was found to be 0.82. Limited findings were drawn on students' understanding of introductory quantum mechanics concepts. Data suggested that the construct of quantum mechanics understanding is most likely multidimensional and the Main Topic defined as "Quantum Mechanics Postulates" may be an especially important factor for students in acquiring a successful understanding of quantum mechanics.
Cataloglu, Erdat
Testing Quantum Mechanics in High-Energy Physics
In this set of lectures we show that particle physics can also contribute to fundamental questions about quantum mechanics\\u000a (QM) and even shine new light in the fine workings of quantum physics and this at scales of energies which are not available\\u000a for usual quantum systems. In particular the massive meson�antimeson systems are specially suitable as they offer a unique
Beatrix C. Hiesmayr
Quantum mechanics model on a K�hler conifold
We propose an exactly solvable model of the quantum oscillator on the class of K�hler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has nonconstant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction
Stefano Bellucci; Armen Nersessian; Armen Yeranyan
OSP Quantum Mechanics: Single Measurments of Spin States Worksheet
NSDL National Science Digital Library
This set of tutorial worksheets, based on the OSP Quantum Mechanics Simulations, help students explore the measurement of quantum spins. The tutorial starts with an introduction of the physics of spins, and then presents the results of a single measurement on pure, mixed, and superposition states.
Belloni, Mario; Christian, Wolfgang
Possibility of a Geometric Constraint in the Schr�dinger Quantum Mechanics
NASA Astrophysics Data System (ADS)
Within the framework of some straightforward mathematical terms it is argued that there exists a space-invariant in the Schr�dinger quantum mechanics (SQM). As an alternative to the geometric features of localized nature dictated by the prescribed boundary conditions in a potential problem in SQM, this spatial invariant is expected to account for some global geometric features of the quantum system.
Kaushal, R. S.
Optical coupling mechanisms in quantum well infrared photodetectors
Light coupling systems such as gratings are required because Quantum Well Infrared Photodetectors do not respond to normal incident light due to the quantum mechanical selection rules associated with intersubband transitions. The resolution of the photolithography and accuracy of the etching become key issues in producing smaller grating feature sizes especially in shorter wavelengths. An enhancement factor of three due
Sumith Bandara; Sarath Gunapala; John Liu; Winn Hong; Jin Park
Elastic, mechanical, and thermodynamical properties of superionic lithium oxide for high pressures
NASA Astrophysics Data System (ADS)
The elastic and thermodynamic properties of Li2O for high pressures are presented. For cubic Li2O, model effective interatomic interaction potential incorporating long-range Coulomb, charge transfer interactions, covalency effect, Hafemeister and Flygare type short-range overlap repulsion extended up to the second neighbor ions and van der Waals interactions is formulated. Both charge transfer interactions and covalency effect apart from long-range Coulomb are important in revealing high-pressure-induced associated volume collapse, elastic, and thermodynamical properties. The elastic constants, Debye temperature, and thermal expansion coefficient obtained are in good agreement with the available experimental data and other theoretical results. The Li2O is mechanically stiffened, thermally softened, and brittle in nature as inferred from the pressure-dependent elastic constants behavior. To our knowledge, this is the first quantitative theoretical prediction of the pressure dependence of elastic, thermal, and thermodynamical properties of Li2O and still awaits experimental confirmation.
Varshney, Dinesh; Shriya, Swarna
A Simplified Quantum Mechanical Model of Diatomic Molecules
ERIC Educational Resources Information Center
Introduces a simple one-dimensional model of a diatomic molecule that can explain all the essential features of a real two particle quantum mechanical system and gives quantitative results in fair agreement with those of a hydrogen molecule. (GA)
Nielsen, Lars Drud
Born series and unitarity in noncommutative quantum mechanics
This paper is dedicated to present model independent results for noncommutative quantum mechanics. We determine sufficient conditions for the convergence of the Born series and, in the sequel, unitarity is proved in full generality.
Bemfica, F. S.; Girotti, H. O. [Instituto de Fisica, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 - Porto Alegre, Rio Grande do Sul (Brazil)
Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation.
National Technical Information Service (NTIS)
This research project was focused on the development of a quantum mechanical balance equation based device simulator that can model advanced, compound, submicron devices, under all transport conditions (AC, DC, and transient response). This report documen...
L. L. Cui
Probabilistic Approach to Teaching the Principles of Quantum Mechanics
ERIC Educational Resources Information Center
Approaches the representation of quantum mechanics through Hilbert space postulates. Demonstrates that if the representation is to be accurate, an evolution operator of the form of a Hamiltonian must be used. (CP)
Santos, Emilio
Quantum mechanical study of sulfuric acid hydration: atmospheric implications.
The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H(2)SO(4)(H(2)O)(n) where n = 1-6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the M�ller-Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO(4)(-)�H(3)O(+))(H(2)O)(n-1) clusters are competitive with the neutral (H(2)SO(4))(H(2)O)(n) clusters for n ? 3 and are more stable than neutral clusters for n ? 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H(2)SO(4)(H(2)O)(n) clusters are favorable in colder regions of the troposphere (T = 216.65-273.15 K) for n = 1-6, but the formation of clusters with n ? 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H(2)SO(4)-H(2)O system must contain more than one H(2)SO(4) and are in concert with recent findings (1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere. PMID:22296037
Temelso, Berhane; Morrell, Thomas E; Shields, Robert M; Allodi, Marco A; Wood, Elena K; Kirschner, Karl N; Castonguay, Thomas C; Archer, Kaye A; Shields, George C
Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics
NASA Astrophysics Data System (ADS)
Quantum tic-tac-toe was developed as a metaphor for the counterintuitive nature of superposition exhibited by quantum systems. It offers a way of introducing quantum physics without advanced mathematics, provides a conceptual foundation for understanding the meaning of quantum mechanics, and is fun to play. A single superposition rule is added to the child's game of classical tic-tac-toe. Each move consists of a pair of marks subscripted by the number of the move (``spooky'' marks) that must be placed in different squares. When a measurement occurs, one spooky mark becomes real and the other disappears. Quantum tic-tac-toe illustrates a number of quantum principles including states, superposition, collapse, nonlocality, entanglement, the correspondence principle, interference, and decoherence. The game can be played on paper or on a white board. A Web-based version provides a refereed playing board to facilitate the mechanics of play, making it ideal for classrooms with a computer projector.
Goff, Allan
Level Comparison Theorems and Supersymmetric Quantum Mechanics.
National Technical Information Service (NTIS)
The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle...
B. Baumgartner H. Grosse A. Martin
Relativistic models of nonlinear quantum mechanics
I present and discuss a class of nonlinear quantum-theory models, based on simple relativistic field theories, in which the parameters depend on the state of the system via expectation values of local functions of the fields.
T. W. B. Kibble
Quantum Mechanics in Biology: Photoexcitations in DNA
\\u000a We consider here the theoretical and quantum chemical description of the photoexcitated states in DNA duplexes. We discuss\\u000a the motivation and limitations of an exciton model and use this as the starting point for more detailed excited state quantum\\u000a chemical evaluations. In particular, we focus upon the role of interbase proton transfer between Watson\\/Crick pairs in localizing\\u000a an excitation and
Eric R. Bittner; Arkadiusz Czader
Mechanism Of The Quantum Speed-up
NASA Astrophysics Data System (ADS)
Bob chooses a function and gives to Alice the black box that computes it. Alice, without knowing Bob's choice, should find a character of the function (e. g. its period) by computing its value for different arguments. There is naturally correlation between Bob's choice and the solution found by Alice. We show that, in quantum algorithms, this correlation becomes quantum. This highlights an overlooked measurement problem: sharing between two completely or partly redundant measurements the determination of completely or partly correlated measurement outcomes. All is like Alice, by reading the solution at the end of the algorithm, contributed to the initial choice of Bob, with half of it in quantum superposition for all the possible ways of taking this half. This contribution, back evolved to before running the algorithm, where Bob's choice is located, becomes Alice knowing in advance half of the choice. The quantum algorithm is the quantum superposition of all the possible ways of taking half of Bob's choice and, given the advanced knowledge of it, classically computing the missing half. The quantum speed-up comes from comparing two classical algorithms, with and without advanced knowledge of half of Bob's choice.
Castagnoli, Giuseppe
Combined quantum and molecular mechanics (QM/MM).
We describe the current state of the art of mixed quantum mechanics/molecular mechanics (QM/MM) methodology, with a particular focus on modeling of enzymatic reactions. Over the past decade, the effectiveness of these methods has increased dramatically, based on improved quantum chemical methods, advances in the description of the QM/MM interface, and reductions in the cost/performance of computing hardware. Two examples of pharmaceutically relevant applications, cytochrome P450 and class C ?-lactamase, are presented.: PMID:24981493
Friesner, Richard A
Testing quantum mechanics in the neutral kaon system
The neutral kaon system is a sensitive probe of quantum mechanics. We revive a parametrization of non-quantum-mechanical effects that is motivated by considerations of the nature of space-time foam, and show how it can be constrained by new measurements of KL-->2pi and KL,S semileptonic decays at LEAR or a phi factory. Permanent address: Center for Theoretical Physics, Department of Physics,
Jonathan Richard Ellis; Nikolaos E Mavromatos; Dimitri V Nanopoulos
Probability in the Many-Worlds Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no "probability" for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: (a) A "sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: "What is the probability of an outcome of a quantum measurement?" with a legitimate question: "What is the probability that `I' am in the world corresponding to that outcome?"; (b) A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and (c) Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and "caring measure" replacing probability measure are discussed.
Vaidman, Lev
Thermodynamics and mechanisms of protonated diglycine decomposition: a computational study.
We present a full computational description of the fragmentation reactions of protonated diglycine (H(+)GG). Relaxed potential energy surface scans performed at B3LYP/6-31�G(d) or B3LYP/6-311?+?G(d,p) levels are used to map the reaction coordinate surfaces and identify the transition states (TSs) and intermediate reaction species for seven reactions observed experimentally in the succeeding companion paper. All structures are optimized at the B3LYP/6-311?+?G(d,p) level, with single point energies of the key optimized structures calculated at B3LYP and MP2(full) levels using a 6-311?+?G(2�d,2p) basis set. These theoretical structures and energies are compared with extensive calculations in the literature. Although the pathways elucidated here are generally in agreement with those previously outlined, new details and, for some reactions, lower energy transition states are located. Further, the mechanism for the combined loss of carbon monoxide and ammonia is explored for the first time. PMID:21952767
Armentrout, P B; Heaton, Amy L
On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.
Lee, Sang-Bong
Sensible Quantum Mechanics:. are Probabilities Only in the Mind?
NASA Astrophysics Data System (ADS)
Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets. These probabilities generally cannot be given by the ordinary quantum �probabilities� for a single set of alternatives. Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth.
Page, Don N.
The Use of Quantum Mechanics in the Treatment of Waveguides
NASA Astrophysics Data System (ADS)
In this paper we give a quantum description of guided waves. A Klein-Gordon type equation is derived for wave propagation in an ideal uniform waveguide, and the appropriate quantum-mechanical interpretation is given. Making use of such methods, we give an analysis of guided waves, of inhomogeneously filled waveguides, of waveguide discontinuities, and generally of passive microwave circuits. A spinorial formalism is employed to derive the equivalent Dirac-type equation. The general applicability of the quantum-mechanical concepts to waveguides is also discussed.
Marinescu, N.
Comparison of Differing Credit Hour Allotments for Thermodynamics and Fluid Mechanics Courses
NSDL National Science Digital Library
Each institution determines how many credit hours will be allotted for each course. Thermodynamics and fluid mechanics in an undergraduate Bachelor of Science Mechanical Engineering curriculum in the United States typically are allotted three or four credit hours. For a semester system, this allows for 42-45 or 56-60 fifty-minute class sessions in three and four credit hour courses, respectively. Opinions vary whether thermodynamics and fluid mechanics should each be three credit hours, each be four credit hours, or one should be three and the other four. Two universities have conducted a study to determine the advantages, disadvantages, and consequences of three vs. four credit hours. One university has a four credit hour thermodynamics and a three credit hour fluid mechanics, while the other university has exactly the opposite. Through student surveys, course objectives/outcomes, course syllabi, instructors experiences, and average grades, conclusions are drawn on the effects of course length. Other issues are examined such as challenges facing instructors who have previously taught a four credit hour course that now must cover the same material within a three credit hour allotment. Finally recommendations are given for instructors that are allotted less than desirable credit hours.
Fletcher, Robert; Gerhart, Andrew; Gerhart, Philip
BOOK REVIEW: Mind, Matter and Quantum Mechanics (2nd edition)
NASA Astrophysics Data System (ADS)
Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic; furthermore there is an asymmetry between the observed and the observing. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, `implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their possible consequences for our understanding of this world (Pauli, Everett, Bohm, Heisenberg). The last section, `new developments', dwells on some ideas about the conscious brain and its possible foundation on quantum mechanics. The book is an interesting and, in part, fascinating contribution to a field that continues to be a companion to `practical' quantum mechanics since its very beginning. It is doubtful whether such types of `quantum ontologies' will ever become (empirically) testable; right now one can hardly expect more than to be offered some consistent `grand picture', which the reader may find more or less acceptable or even rewarding. Many practicing quantum physicists, though, will remain unimpressed. The shift from synthetic ontology to analytic ontology is the foundation of the present work. This means that fundamental wholes are being partitioned into their ontologically subordinate components by means of `events'. The actual event, in turn, is an abrupt change in the Heisenberg state describing the quantum universe. The new state then defines the tendencies associated with the next actual event. To avoid infinite regression in terms of going from one state of tendencies to the next, consciousness is there to give these events a special `feel', to provide a status of `intrinsic actuality'. The brain of an alert human observer is similar in an important way to a quantum detection device: it can amplify small signals to large macroscopic ef
Mahler, G.
Quantum mechanical states as attractors for Nelson processes
NASA Astrophysics Data System (ADS)
In this paper we reconsider, in the light of the Nelson stochastic mechanics, the idea originally proposed by Bohm and Vigier that arbitrary solutions of the evolution equation for the probability densities always relax in time toward the quantum mechanical density �?�2 derived from the Schr�dinger equation. The analysis of a few general propositions and of some physical examples show that the choice of the L1 metrics and of the Nelson stochastic flux is correct for a particular class of quantum states, but cannot be adopted in general. This indicates that the question if the quantum mechanical densities attract other solution of the classical Fokker-Planck equations associated to the Schr�dinger equation is physically meaningful, even if a classical probabilistic model good for every quantum stale is still not available. A few suggestion in this direction are finally discussed.
Petroni, Nicola Cufaro; Guerra, Francesco
Kink mass quantum shifts from SUSY quantum mechanics
NASA Astrophysics Data System (ADS)
In this paper a new version of the DHN (Dashen-Hasslacher-Neveu) formula, which is used to compute the one-loop order kink mass correction in (1+1)-dimensional scalar field theory models, is constructed. The new expression is written in terms of the spectral data coming from the supersymmetric partner operator of the second-order small kink fluctuation operator and allows us to compute the kink mass quantum shift in new models for which this calculation was out of reach by means of the old formula.
Izquierdo, Alberto Alonso; Guilarte, Juan Mateos; Plyushchay, Mikhail S.
Multiple-event probability in general-relativistic quantum mechanics
We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.
Hellmann, Frank [Fakultaet fuer Physik, Ludwig-Maximilians-Universitaet, D-80799 Munich (Germany); Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille (France); Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo [Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille (France)
'Mysticism' in quantum mechanics: the forgotten controversy
NASA Astrophysics Data System (ADS)
This paper argues that a European controversy over a 'mystical' hypothesis, one assigning the mind a role to play at the material level of reality, shaped much of the debate over the interpretation of the quantum equations. It traces back the controversy to the past two decades, beginning in the late 1920s�birth of quantum theory�and concluding with Erwin Schr�dinger's lectures published as 'Mind and Matter'. Becoming aware of the issues at stake can help us understand the historical, philosophical and cultural background from which today's physics emerged.
Marin, Juan Miguel
Free energies of binding from large-scale first-principles quantum mechanical calculations: application to ligand hydration energies.
Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program. PMID:23841453
Fox, Stephen J; Pittock, Chris; Tautermann, Christofer S; Fox, Thomas; Christ, Clara; Malcolm, N O J; Essex, Jonathan W; Skylaris, Chris-Kriton
Evading Quantum Mechanics: Engineering a Classical Subsystem within a Quantum Environment
NASA Astrophysics Data System (ADS)
Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement backaction often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that, by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement backaction of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, backaction evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical-force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broadband squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic-spin ensembles, and implementations of the quantum Toffoli gate.
Tsang, Mankei; Caves, Carlton M.
Quantum mechanics with spontaneous localization and the quantum theory of measurement
Summary��Quantum mechanics with spontaneous localization (QMSL) is a recently proposed stochastic modification of theN-body Schr�dinger equation consistent both with microphysics and macrophysics. QMSL is applied here to the measurement problem.\\u000a It is shown that the replacement of standard quantum mechanics by QMSL has the only effect of producing an actual reduction\\u000a of the wave function.
F. Benatti; G. C. Ghirardi; A. Rimini; T. Weber
The Transactional Interpretation of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Preface; 1. Introduction: quantum peculiarities; 2. The map vs the territory; 3. The original TI: fundamentals; 4. The new possibilist TI: fundamentals; 5. Challenges, replies, and applications; 6. PTI and relativity; 7. The metaphysics of possibility; 8. PTI and 'spacetime'; 9. Epilogue: more than meets the eye; Appendixes; References; Index.
Kastner, Ruth E.
Many of the most familiar features of our everyday environment, and some of our basic notions about it, stem from Relativistic Quantum Field Theory (RQFT). We argue in particular that the origin of common names, verbs, adjectives such as full and empty, the concepts of identity, similar- ity, Plato's Universals, natural numbers, and existence versus non-existence can be traced to
Cihan Sacl�oglu
Quantum mechanics on profinite groups and partial order
NASA Astrophysics Data System (ADS)
Inverse limits and profinite groups are used in a quantum mechanical context. Two cases are considered: a quantum system with positions in the profinite group { {Z}}_p and momenta in the group { {Q}}_p/{ {Z}}_p, and a quantum system with positions in the profinite group {\\widehat{ {Z}}} and momenta in the group { {Q}}/{ {Z}}. The corresponding Schwatz-Bruhat spaces of wavefunctions and the Heisenberg-Weyl groups are discussed. The sets of subsystems of these systems are studied from the point of view of partial order theory. It is shown that they are directed-complete partial orders. It is also shown that they are topological spaces with T0-topologies, and this is used to define continuity of various physical quantities. The physical meaning of profinite groups, non-Archimedean metrics, partial orders and T0-topologies, in a quantum mechanical context, is discussed.
Vourdas, A.
EDITORIAL: Focus on Mechanical Systems at the Quantum Limit FOCUS ON MECHANICAL SYSTEMS AT THE QUANTUM LIMIT
NASA Astrophysics Data System (ADS)
The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds�the authors of this editorial are a representative sample�has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the diverse backgrounds and approaches of the researchers. As diverse as the approaches are the manifold of goals and perspectives for operating mechanical systems close to or within the quantum regime. Already now, nanomechanical sensors achieve single-molecule mass detection and magnetic resonance force detection from single-electron spins although they are operated far from quantum. Quantum-limited mechanical devices promise a new technology with hitherto unachieved performance for high-resolution sensing. This is also of high relevance for macroscopic mechanical resonators used in gravitational wave detectors. Furthermore, the increasing capability to couple mechanical modes to individual quantum systems raises the interesting question of whether mechanics can serve as a quantum bus in hybrid implementations of quantum information processing. Finally, the possibility of generating quantum superposition states that involve displacements of a massive macroscopic object (such as the center of mass of a mechanical beam) provides a completely new parameter regime for testing quantum theory over the amazing range from nanomechanical objects of several picograms up to gram-scale mirrors used in gravitational wave interferometers. We are looking forward to these fascinating developments! This Focus Issue is intended to highlight the present status of the field and to provide both introduction and motivation for students and researchers who want to get familiar with this exciting area or even want to join it. It also complements the conference activities of our community during the last year, where a series of dedicated invited sessions at several international conferences (APS March Meeting 2008, CLEO/QELS 2008, OSA Frontiers in Optics 2008, PQE 2008/2009 etc) culminated in the first Gordon Conference on 'Mechanical Systems at the Quantum Limit'. Given the fast development of the field it was not surprising to see that during the collection of the following contributions new progress was reported almost on a monthly basis and new groups entered the field. We intend to
Aspelmeyer, Markus; Schwab, Keith
A formal derivation of the Gibbs entropy for classical systems following the Schr�dinger quantum mechanical approach
NASA Astrophysics Data System (ADS)
In the traditional statistical mechanics textbooks, the entropy concept is first introduced for the microcanonical ensemble and then extended to the canonical and grand-canonical cases. However, in the authors' experience, this procedure makes it difficult for the student to see the bigger picture and, although quite ingenuous, the subtleness of the demonstrations to pass from the microcanonical to the canonical and grand-canonical ensembles is hard to grasp. In the present work, we adapt the approach used by Schr�dinger to introduce the entropy definition for quantum mechanical systems to derive a classical mechanical entropy definition, which is valid for all ensembles and is in complete agreement with the Gibbs entropy. Afterwards, we show how the specific probability densities for the microcanonical and canonical ensembles can be obtained from the system macrostate, the entropy definition and the second law of thermodynamics. After teaching the approach introduced in this paper for several years, we have found that it allows a better understanding of the statistical mechanics foundations. On the other hand, since it demands previous knowledge of thermodynamics and mathematical analysis, in our experience this approach is more adequate for final-year undergraduate and graduate physics students.
Santill�n, M.; Zeron, E. S.; DelRio-Correa, J. L.
Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'
A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ''smuggled'' in. That argument is examined here and shown, I believe, to be defective.
Stapp, H.P.
Some thoughts about consciousness: from a quantum mechanics perspective.
The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantum mechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning. PMID:23865992
Gargiulo, Gerald J
ysteries, Puzzles, and Paradoxes in Quantum Mechanics. Proceedings
These proceedings represent papers presented at the Mysteries, Puzzles, and Paradoxes in Quantum Mechanics Workshop held in Italy, in August 1998. The Workshop was devoted to recent experimental and theoretical advances such as new interference, effects, the quantum eraser, non{minus}disturbing and Schroedinger{minus}cat{minus}like states, experiments, EPR correlations, teleportation, superluminal effects, quantum information and computing, locality and causality, decoherence and measurement theory. Tachyonic information transfer was also discussed. There were 45 papers presented at the conference,out of which 2 have been abstracted for the Energy,Science and Technology database.(AIP)
Rodolfo, B. [Department of Physics, University of Milan, (Italy)
Maximum-power quantum-mechanical Carnot engine
In their work [J. Phys. AJPHAC50305-447010.1088\\/0305-4470\\/33\\/24\\/302 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through changes of both the width of the well and the quantum state in a specific manner.
Sumiyoshi Abe
On the relation between classical and quantum statistical mechanics
Classical and quantum statistical mechanics are compared in the high temperature limit ?=1\\/kT?0. While this limit is rather trivial for spin systems, we obtain some rigorous results which suggest (and sometimes prove) different asymptotics for continuous systems, depending on the behaviour of the two-body potential for small distances: the difference between suitable classical and quantum variables vanishes as ?2 for
W. Wreszinski; G. Scharf
Quantum Mechanics Emerges from Information Theory Applied to Causal Horizons
NASA Astrophysics Data System (ADS)
It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde's entropic gravity theory is also investigated.
Lee, Jae-Weon
Quantum mechanics from an equivalence principle
The authors show that requiring diffeomorphic equivalence for one-dimensional stationary states implies that the reduced action S{sub 0} satisfies the quantum Hamilton-Jacobi equation with the Planck constant playing the role of a covariantizing parameter. The construction shows the existence of a fundamental initial condition which is strictly related to the Moebius symmetry of the Legendre transform and to its involutive character. The universal nature of the initial condition implies the Schroedinger equation in any dimension.
Faraggi, A.E. [Univ. of Florida, Gainesville, FL (United States). Inst. for Fundamental Theory; Matone, M. [Univ. of Padova (Italy)
Investigations of fundamental phenomena in quantum mechanics with neutrons
NASA Astrophysics Data System (ADS)
Neutron interferometer and polarimeter are used for the experimental investigations of quantum mechanical phenomena. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics � la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit. At last, as an example of a counterfactual phenomenon of quantum mechanics, observation of so-called quantum Cheshire Cat is carried out by using neutron interferometer. Experimental results suggest that pre- and post-selected neutrons travel through one of the arms of the interferometer while their magnetic moment is located in the other arm.
Hasegawa, Yuji
PREFACE: Progress in supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
The theory of integrable systems is grounded in the very beginning of theoretical physics: Kepler's system is an integrable system. This field of dynamical systems, where one looks for exact solutions of the equations of motion, has attracted most of the great figures in mathematical physics: Euler, Lagrange, Jacobi, etc. Liouville was the first to formulate the precise mathematical conditions ensuring solvability `by quadrature' of the dynamical equations, and his theorem still lies at the heart of the recent developments. The modern era started about thirty years ago with the systematic formulation of soliton solutions to nonlinear wave equations. Since then, impressive developments arose both for the classical and the quantum theory. Subtle mathematical techniques were devised for the resolution of these theories, relying on algebra (group theory), analysis and algebraic geometry (Riemann theory of surfaces). We therefore clearly see that the theory of integrable systems lies ab initio at a crossing of physics and mathematics, and that the developments of these last thirty years have strengthened this dual character, which makes it into an archetypal domain of mathematical physics. As regards the classical theory, beyond the direct connections to the various domains of classical soliton physics (hydrodynamics, condensed matter physics, laser optics, particle physics, plasma, biology or information coding), one has witnessed in these recent years more unexpected (and for some of them not yet well understood) connections to a priori farther fields of theoretical physics: string theory (through matrix models), topological field theories (two dimensional Yang--Mills, three dimensional Chern--Simons--Witten), or supersymmetric field theories (for instance the correspondence discovered by Seiberg and Witten between classical integrable models and quantum potentials). Quantum integrable theories provide examples of exactly (non perturbatively) solvable physical models. They thus allow one to obtain descriptions of non trivial phenomena such as second order phase transition in condensed systems (spin lattices) and exact solution of relativistic quantum field theories (Sine--Gordon...). On the other hand, they supply an excellent example of fruitful interface between physics and mathematics: the theory of quantum groups (and the germane theory of special functions) is a perfect illustration of this r�le and perspectives of such new developments appear very promising. The purpose of the first RAQIS meeting was to bring together researchers from the various fields of mathematics and physics connected to the theory of quantum integrable systems. This conference was held in the framework of the European TMR network EUCLID `Integrable models and applications: from strings to condensed matter', contract number HPRN-CT-2002-00325. The RAQIS03 meeting took place at the Laboratoire d'Annecy-le-vieux de Physique Th�orique (LAPTH, France) from 25 March to 28 March, 2003. The organising committee consisted of Daniel Arnaudon, Jean Avan, Luc Frappat, �ric Ragoucy and Paul Sorba. Financial support was provided by Universit� de Savoie and CNRS-DRI (Centre National de la Recherche Scientifique, Direction des Relations Internationales). In particular various scientific contacts with several Japanese participants were initiated thanks to the CNRS PICS contract number 911. This special issue of Journal of Physics A: Mathematical and General is dedicated to the subject of the RAQIS03 meeting in Annecy-le-vieux. Most of the contributors to this issue took part in the meeting, but this volume does not aim to be a proceedings in the usual sense of the word: contributions do not necessarily coincide with the reports presented at the meeting, nor are the contributors restricted exclusively to those people that were present. The intention of the special issue is to benefit from the occasion offered by the RAQIS03 meeting to highlight the important new areas in quantum integrability, by collecting together in one single volume a selection of article
Aref'eva, I.; Fern�ndez, D. J.; Hussin, V.; Negro, J.; Nieto, L. M.; Samsonov, B. F.
On the complexity of classical and quantum algorithms for numerical problems in quantum mechanics
NASA Astrophysics Data System (ADS)
Our understanding of complex quantum mechanical processes is limited by our inability to solve the equations that govern them except for simple cases. Numerical simulation of quantum systems appears to be our best option to understand, design and improve quantum systems. It turns out, however, that computational problems in quantum mechanics are notoriously difficult to treat numerically. The computational time that is required often scales exponentially with the size of the problem. One of the most radical approaches for treating quantum problems was proposed by Feytiman in 1982 [46]: he suggested that quantum mechanics itself showed a promising way to simulate quantum physics. This idea, the so called quantum computer, showed its potential convincingly in one important regime with the development of Shor's integer factorization algorithm which improves exponentially on the best known classical algorithm. In this thesis we explore six different computational problems from quantum mechanics, study their computational complexity and try to find ways to remedy them. In the first problem we investigate the reasons behind the improved performance of Shor's and similar algorithms. We show that the key quantum part in Shor's algorithm, the quantum phase estimation algorithm, achieves its good performance through the use of power queries and we give lower bounds for all phase estimation algorithms that use power queries that match the known upper bounds. Our research indicates that problems that allow the use of power queries will achieve similar exponential improvements over classical algorithms. We then apply our lower bound technique for power queries to the Sturm-Liouville eigenvalue problem and show matching lower bounds to the upper bounds of Papageorgiou and Wozniakowski [85]. It seems to be very difficult, though, to find nontrivial instances of the Sturm-Lionville problem for which power queries can be simulated efficiently. A quantum computer differs from a classical computer that uses randomness, because it allows "negative probabilities" that can cancel each other (destructive interference). Ideally we would like to transfer classical randomized algorithms to the quantum computer and get speed improvements. One of the simplest classical randomized algorithm is the random walk and we study the behavior of the continuous-time quantum random walk. We analyze this random walk in one dimension and give analytical formulas for its behavior that demonstrate its interference properties. Is interference or cancellation really the most important advantage that a quantum computer has over a classical computer? To answer that question we study the class StociMA of "stochastic quantum" algorithms that only use classical gates, but are given a quantum "witness", i.e. an arbitrary quantum state that can guide the algorithm in computing the correct answer, but should not be able to "fool" it. We show that there exists a complete problem for this class, which we call the stoquastic local Hamiltonian problem. In this problem we try to compute the lowest eigenvalue of a Hamiltonian with interactions that span only a fixed number of particles and all contribute negatively. With the help of this problem we prove that MA ? StocIMA ? SBP ? QMA. This shows that interference is one of the most important parts of quantum computation. The simulation of the evolution of a general quantum system in time requires a computational time that is exponential in the dimension of the system. But maybe the problem that we ask for is too general and we can simulate special systems in polynomial time. In particular it would be interesting to study quantum systems of "limited energy", i.e. for which the state at starting time consists mainly out of components with small energy. We model this in the theory of weighted reproducing kernel Hilbert spaces with two different sets of weights: product weights and finite-order weights. We will show that the information cost of computing the evolution for start
Bessen, Arvid J.
Structure, thermodynamics, mechanical properties and glassy dynamics in anisotropic polymeric materials
NASA Astrophysics Data System (ADS)
Anisotropic polymeric materials are ubiquitous. They can form via self assembly, external mechanical deformation or by geometric confinement. Important examples of anisotropic polymeric materials include liquid crystalline polymers and elastomers, amorphous rubber networks, confined films and grafted polymer brushes. A common feature of these materials is the anisotropic conformation of the constituent polymer chains which leads to significant modification of interchain packing correlations and thermodynamics properties. Polymer liquid state statistical mechanical methods have been generalized to treat the structure, segmental orientation, thermodynamics and mechanical response of dense polymer fluids and crosslinked networks. The consequences of interchain repulsions and chain connectivity are explicitly taken into account. The strain-induced orientational order parameter of flexible chains is predicted to scale as the inverse of the square root of the degree of polymerization and increase in a supralinear manner with segmental concentration. Two nonclassical contributions to stress and linear modulus arise from the influence of anisotropic packing correlations on the excess free energy. Overall the theory is in good agreement with NMR and mechanical experiments and computer simulations. The thermomechanical properties of nematic elastomers have also been studied. Significant softening of the modulus is found as the isotropic-nematic transition is approached. The phenomenon of spontaneous distortion, relevant to artificial muscles, sensors and actuator applications, emerges in a manner correlated directly with the orientational order parameter. Comparison of our theoretical predictions with experiments on thermotropic liquid crystalline polymers shows good qualitative and semi-quantitative agreements. A dynamical theory has been developed for the onset or crossover temperature (Tc) to highly non-Arrenhius activated relaxation regime in deeply supercooled polymer liquids. Alignment and/or deformation modify thermodynamic and structural properties thereby inducing anisotropic segmental dynamics. Either suppression or elevation of ( Tc) is predicted depending on the nature of anisotropy. Results have been obtained for liquid crystalline polymers, thin films, rubber networks and grafted polymer brushes. The underlying mechanism for ( Tc) shifts is this theory is anisotropy of the degree of coil interpenetration.
Oyerokun, Folusho Taiwo
A deformation quantization theory for noncommutative quantum mechanics
We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].
Costa Dias, Nuno; Prata, Joao Nuno [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal) and Grupo de Fisica Matematica, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal); Gosson, Maurice de [NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria); Luef, Franz [NuHAG Fakultaet fuer Mathematik, Universitaet Wien, Wien 1090 (Austria); Department of Mathematics, UC Berkeley, 847 Evans Hall, Berkeley, California 94720-3840 (United States)
Weyl-Wigner formulation of noncommutative quantum mechanics
We address the phase-space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativities. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Darboux map, we construct an isomorphism between the operator and the phase-space representations of the extended Heisenberg algebra. This map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space. We construct the extended star product and Moyal bracket and propose a general definition of noncommutative states. We study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of the Darboux map. Our approach unifies and generalizes all the previous proposals for the phase-space formulation of noncommutative quantum mechanics. For concreteness we rederive these proposals by restricting our formalism to some two-dimensional spaces.
Bastos, Catarina; Bertolami, Orfeu [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Dias, Nuno Costa; Prata, Joao Nuno [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Av. Campo Grande, 376, 1749-024 Lisboa (Portugal)
Quantum-mechanical transport equation for atomic systems.
NASA Technical Reports Server (NTRS)
A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.
Berman, P. R.
Nambu quantum mechanics on discrete 3-tori
NASA Astrophysics Data System (ADS)
We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus \\mathbb{T}_N^3 represented by elements of the group SL(3,\\mathbb{Z}_N) . These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three-dimensional toroidal phase space and are characterized by invariant vectors a of \\mathbb{T}_N^3 . We quantize all such flows, which are necessarily restricted on a planar two-dimensional phase space, embedded in the 3-torus, transverse to the vector a. The corresponding maps belong to the little group of \\bm{a} \\in SL(3,\\mathbb{Z}_N) , which is an SL(2,\\mathbb{Z}_N) subgroup. The associated linear Nambu maps are generated by a pair of linear and quadratic Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding quantum maps realize the metaplectic representation of SL(3,\\mathbb{Z}_N) on the discrete group of three-dimensional magnetic translations, i.e. the non-commutative 3-torus with a deformation parameter the Nth root of unity. Other potential applications of our construction are related to the quantization of deterministic chaos in turbulent maps as well as to quantum tomography of three-dimensional objects.
Axenides, M.; Floratos, E. G.; Nicolis, S.
Quantum mechanisms of density wave transport.
We report on new developments in the quantum picture of correlated electron transport in charge and spin density waves. The model treats the condensate as a quantum fluid in which charge soliton domain wall pairs nucleate above a Coulomb blockade threshold field. We employ a time-correlated soliton tunneling model, analogous to the theory of time-correlated single electron tunneling, to interpret the voltage oscillations and nonlinear current-voltage characteristics above threshold. An inverse scaling relationship between threshold field and dielectric response, originally proposed by Gr�ner, emerges naturally from the model. Flat dielectric and other ac responses below threshold in NbSe(3) and TaS(3), as well as small density wave phase displacements, indicate that the measured threshold is often much smaller than the classical depinning field. In some materials, the existence of two distinct threshold fields suggests that both soliton nucleation and classical depinning may occur. In our model, the ratio of electrostatic charging to pinning energy helps determine whether soliton nucleation or classical depinning dominates. PMID:22711979
Miller, John H; Wijesinghe, Asanga I
Study on a Possible Darwinian Origin of Quantum Mechanics
NASA Astrophysics Data System (ADS)
A sketchy subquantum theory deeply influenced by Wheeler's ideas (Am. J. Phys. 51:398-404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics from these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered.
Baladr�n, C.
Conceptual and mathematical barriers to students learning quantum mechanics
NASA Astrophysics Data System (ADS)
Quantum mechanics has revolutionized the way we view the physical world. This theory has required a dramatic revision in the structure of the laws of mechanics governing the behavior of the particles and led to the discovery of macroscopic quantum effects ranging from lasers and superconductivity to neutron stars and radiation from black holes. Though its validity is well confirmed by the experimental evidence available, quantum mechanics remains somewhat of a mystery. The purpose of this study is to identify students' conceptual and mathematical difficulties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these difficulties. We have investigated student understanding of several core topics in the introductory courses, including quantum measurement, probability, Uncertainty Principle, wave functions, energy eigenstates, recognizing symmetry in physical systems, and mathematical formalism. Student specific difficulties with these topics are discussed throughout this dissertation. In addition, we have studied student difficulties in learning, applying, and making sense out of complex mathematical processes in the physics classroom. We found students' achievement in quantum courses is not independent of their math backgrounds (correlation coefficient 0.547 for P631 and 0.347 for P263). In addition, there is a large jump in the level of mathematics at which one needs to succeed in physics courses after the sophomore level in The Ohio State University's physics curriculum. Many students do not have a functional understanding of probability and its related terminologies. For example, many students confuse the "expectation value" with "probability density" in measurement and some students confuse "probability density" with "probability amplitude" or describe the probability amplitude as a "place" or "area." Our data also suggested that students tend to use classical models when interpreting quantum systems; for example, some students associate a higher energy to a larger amplitude in a wave function. Others, have difficulty differentiating wave functions from energy eigenstates. Furthermore, some students do not use the relationship between the wave function and the wavenumber as a primary resource in for qualitative analysis of wave functions in regions of different potential. Many students have difficulty recognizing mathematical symbols for a given graph and lack the ability to associate the correct functions with their respective graphs. I addition, students do not distinguish an oscillatory function such as e-ix from an exponential decay function such as e-x. The results reported suggest recommendations for further study of student understanding of quantum mechanics and for the development of materials to aid understanding. These recommendations have potentially important implications for the teaching of introductory quantum mechanics and for the development of teaching aids, texts, and technology resources.
Sadaghiani, Homeyra R.
Quantum mechanical point of view to perturbative problems in classical mechanics.
National Technical Information Service (NTIS)
This paper shows that perturbative methods currently exploited in quantum mechanics can be used to treat a classical Liouville problem describing the evolution of an ensemble of non-collisional particles. The method we discuss is based on the introduction...
G. Dattoli A. Torre
Theoretical studies on the vibrational spectra, thermodynamic properties, detonation properties, and pyrolysis mechanisms for polynitroadamantanes.
To look for high energy density materials (HEDM), the relationships between the structures and the performances of polynitroadamantanes (PNAs) were studied. The assigned infrared spectra of PNAs obtained at the density functional theory (DFT) B3LYP/6-31G level were used to compute the thermodynamic properties on the basis of the principle of statistical thermodynamics. The thermodynamic properties are linearly related with the number of nitro groups as well as with the temperatures. Detonation properties of PNAs were evaluated by using the Kamlet-Jacobs equation based on the calculated densities and heats of formation for titled compounds, and it is found that only when the number of nitro groups of PNA is equal to or more than eight can it be possible for PNAs to be used as HEDMs. The relative stabilities of PNAs were studied by the pyrolysis mechanism using the UHF-PM3 method. The homolysis of the C-NO2 bond is predicted to be the initial step of thermal decomposition. The activation energies (Ea) for the homolysis decrease with the number of nitro groups being increased on the whole. The stability order of dinitroadamantane isomers derived from the interactions among nitro groups is consistent with what is determined by Ea. The relations between the Ea's and the electronic structure parameters were discussed. In combination with the stability, PNA (1,2,3,4,5,6,7,8,9,10-) is recommended as the target of HEDM with insensitivity. PMID:16331911
Xu, Xiao Juan; Xiao, He Ming; Gong, Xue Dong; Ju, Xue Hai; Chen, Zhao Xu
Exactly constructing model of quantum mechanics with random environment
Dissipation and decoherence, interaction with the random media, continuous measurements and many other complicated problems of open quantum systems are a result of interaction of quantum system with the random environment. These problems mathematically are described in terms of complex probabilistic processes (CPP). Note that CPP satisfies the stochastic differential equation (SDE) of Langevin-Schroedinger(L-Sch)type, and is defined on the extended space R{sup 1} - R{sub {l_brace}{gamma}{r_brace}}, where R{sup 1} and R{sub {l_brace}{gamma}{r_brace}} are the Euclidean and the functional spaces, correspondingly. For simplicity, the model of 1D quantum harmonic oscillator (QHO) with the stochastic environment is considered. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. By S DM method, the thermodynamical potentials, such as the nonequilibrium entropy and the energy of the 'ground state' are constructed in a closed form. The expressions for uncertain relations and Wigner function depending on interaction's constant between 1D QHO and the environment are obtained.
Gevorkyan, A. S., E-mail: firstname.lastname@example.com [IIAP NAS of Armenia (Armenia)
The Quantum and Klein-Gordon Oscillators in a Non-commutative Complex Space and the Thermodynamic Functions
NASA Astrophysics Data System (ADS)
In this work we study the quantum and Klein-Gordon oscillators in a non-commutative complex space. We show that a particle described by such oscillators behaves similarly as an electron with spin in a commutative space in an external uniform magnetic field. Therefore the wave-function takes values in C 4, spin up, spin down, particle, antiparticle, a result which is obtained by the Dirac theory. We obtain the energy levels by exact solutions. We also derive the thermodynamic functions associated to the partition function, and show that the non-commutativity effects are manifested in energy at the high temperature limit.
Zaim, Slimane
Conceptual and Mathematical Barriers to Students Learning Quantum Mechanics
NSDL National Science Digital Library
The purpose of this study is to identify students' conceptual and mathematical difficulties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these difficulties. We have investigated student understanding of several core topics in the introductory courses, including quantum measurement, probability, Uncertainty Principle, wave functions, energy eigenstates, recognizing symmetry in physical systems, and mathematical formalism. Student specific difficulties with these topics are discussed throughout this dissertation. In addition, we have studied student difficulties in learning, applying, and making sense out of complex mathematical processes in the physics classroom. We found students' achievement in quantum courses is not independent of their math backgrounds. In addition, there is a large jump in the level of mathematics at which one needs to succeed in physics courses after the sophomore level in The Ohio State University's physics curriculum. The results reported suggest recommendations for further study of student understanding of quantum mechanics and for the development of materials to aid understanding. These recommendations have potentially important implications for the teaching of introductory quantum mechanics and for the development of teaching aids, texts, and technology resources.
Sadaghiani, Homeyra R.
Quantum mechanical force field for water with explicit electronic polarization.
A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 � 10(6) self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes. PMID:23927266
Han, Jaebeom; Mazack, Michael J M; Zhang, Peng; Truhlar, Donald G; Gao, Jiali
Quantum mechanical force field for water with explicit electronic polarization
A quantum mechanical force field (QMFF) for water is described. Unlike traditional approaches that use quantum mechanical results and experimental data to parameterize empirical potential energy functions, the present QMFF uses a quantum mechanical framework to represent intramolecular and intermolecular interactions in an entire condensed-phase system. In particular, the internal energy terms used in molecular mechanics are replaced by a quantum mechanical formalism that naturally includes electronic polarization due to intermolecular interactions and its effects on the force constants of the intramolecular force field. As a quantum mechanical force field, both intermolecular interactions and the Hamiltonian describing the individual molecular fragments can be parameterized to strive for accuracy and computational efficiency. In this work, we introduce a polarizable molecular orbital model Hamiltonian for water and for oxygen- and hydrogen-containing compounds, whereas the electrostatic potential responsible for intermolecular interactions in the liquid and in solution is modeled by a three-point charge representation that realistically reproduces the total molecular dipole moment and the local hybridization contributions. The present QMFF for water, which is called the XP3P (explicit polarization with three-point-charge potential) model, is suitable for modeling both gas-phase clusters and liquid water. The paper demonstrates the performance of the XP3P model for water and proton clusters and the properties of the pure liquid from about 900 � 10{sup 6} self-consistent-field calculations on a periodic system consisting of 267 water molecules. The unusual dipole derivative behavior of water, which is incorrectly modeled in molecular mechanics, is naturally reproduced as a result of an electronic structural treatment of chemical bonding by XP3P. We anticipate that the XP3P model will be useful for studying proton transport in solution and solid phases as well as across biological ion channels through membranes.
Han, Jaebeom; Mazack, Michael J. M.; Zhang, Peng; Truhlar, Donald G.; Gao, Jiali [Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455-0431 (United States)] [Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455-0431 (United States)
Hilbert space for quantum mechanics on superspace
In superspace a realization of sl{sub 2} is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl{sub 2}-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.
Coulembier, K.; De Bie, H. [Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Krijgslaan 281, 9000 Gent (Belgium)
Hilbert space for quantum mechanics on superspace
NASA Astrophysics Data System (ADS)
In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.
Coulembier, K.; de Bie, H.
The quantum mechanics of perfect fluids
NASA Astrophysics Data System (ADS)
We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vortex degrees of freedom. On the one hand, these have formally a vanishing strong-coupling energy scale, thus suggesting that the effective theory's regime of validity is vanishingly narrow. On the other hand, we prove an analog of Coleman's theorem, whereby the semiclassical vacuum has no quantum counterpart, thus suggesting that the vortex premature strong-coupling phenomenon stems from a bad identification of the ground state and of the perturbative degrees of freedom. Finally, vortices break the usual connection between short distances and high energies, thus potentially impairing the unitarity of the effective theory.
Endlich, Solomon; Nicolis, Alberto; Rattazzi, Riccardo; Wang, Junpu
On the Lattice Structure of Probability Spaces in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Let {C} be the set of all possible quantum states. We study the convex subsets of {C} with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.
Holik, Federico; Massri, C�sar; Plastino, A.; Zuberman, Leandro
PREFACE: EmQM13: Emergent Quantum Mechanics 2013
NASA Astrophysics Data System (ADS)
These proceedings comprise the invited lectures of the second international symposium on Emergent Quantum Mechanics (EmQM13), which was held at the premises of the Austrian Academy of Sciences in Vienna, Austria, 3�6 October 2013. The symposium was held at the ''Theatersaal'' of the Academy of Sciences, and was devoted to the open exploration of emergent quantum mechanics, a possible ''deeper level theory'' that interconnects three fields of knowledge: emergence, the quantum, and information. Could there appear a revised image of physical reality from recognizing new links between emergence, the quantum, and information? Could a novel synthesis pave the way towards a 21st century, ''superclassical'' physics? The symposium provided a forum for discussing (i) important obstacles which need to be overcome as well as (ii) promising developments and research opportunities on the way towards emergent quantum mechanics. Contributions were invited that presented current advances in both standard as well as unconventional approaches to quantum mechanics. The EmQM13 symposium was co�organized by Gerhard Gr�ssing (Austrian Institute for Nonlinear Studies (AINS), Vienna), and by Jan Walleczek (Fetzer Franklin Fund, USA, and Phenoscience Laboratories, Berlin). After a very successful first conference on the same topic in 2011, the new partnership between AINS and the Fetzer Franklin Fund in producing the EmQM13 symposium was able to further expand interest in the promise of emergent quantum mechanics. The symposium consisted of two parts, an opening evening addressing the general public, and the scientific program of the conference proper. The opening evening took place at the Great Ceremonial Hall (Grosser Festsaal) of the Austrian Academy of Sciences, and it presented talks and a panel discussion on ''The Future of Quantum Mechanics'' with three distinguished speakers: Stephen Adler (Princeton), Gerard 't Hooft (Utrecht) and Masanao Ozawa (Nagoya). The articles contained in these proceedings represent the talks of the invited speakers as written immediately after the symposium. The volume starts with a contribution by organizers Jan Walleczek and Gerhard Gr�ssing, essentially explaining why emergent quantum mechanics, and other deterministic approaches to quantum theory, must be considered viable approaches in quantum foundations today. This is followed by the exposition of Stephen Adler's talk who introduced to a general audience key questions at the current frontiers of quantum mechanics during the opening evening (with the contents of his conference talk appearing elsewhere). The conference proceedings then continues with the presentations as given in their chronological order i.e. starting with the opening talk of the scientific program by Gerard 't Hooft. While the page number was restricted for all invited speakers, the paper by Jeff Tollaksen was given more space, as his invited collaborator Yakir Aharonov was unable to deliver a separate talk, in order to represent both contributions in one paper. Note that the talks of all speakers, including the talks of those who could not be represented in this volume (M. Arndt, B. Braverman, C. Brukner, S. Colin, Y. Couder, B. Poirier, A. Steinberg, G. Weihs and H. Wiseman) are freely available on the conference website as video presentations (http://www.emqm13.org). The organizers wish to express their gratitude to Siegfried Fussy and Herbert Schwabl from AINS for the organizational support. The organizers also wish to thank Bruce Fetzer, President and CEO, John E. Fetzer Memorial Trust, and the Members of the Board of Trustees, for their strong support and for funding this symposium. We also wish to thank the Austrian Academy of Sciences for allowing the symposium to be held on their premises, and Anton Zeilinger, President of the Austrian Academy of Sciences, for his welcome address. The expertise of the Members of the Scientific Advisory Board of the EmQM13 symposium, Ana Maria Cetto (Mexico), Lajos Di�si (Budapest), Maurice de Gosson (Vienna), Edward Nelson (Princeton), The
Surveying students' understanding of quantum mechanics in one spatial dimension
NSDL National Science Digital Library
We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and administered it to more than 200 students at 10 institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, and the time-dependence of the wavefunction and expectation values. We find that undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The findings also suggest that graduate quantum mechanics courses may not be effective at helping students to develop a better conceptual understanding of these topics, partly because such courses mainly focus on quantitative assessments.
Zhu, Guangtian; Singh, Chandralekha
Modelling the formation of high aspect CdSe quantum wires: axial-growth versus oriented-attachment mechanisms
NASA Astrophysics Data System (ADS)
Following the recent low temperature synthesis of high quality and single crystal CdSe quantum nanowires, we have used a thermodynamic model to investigate the plausibility of axial-growth and oriented-attachment formation mechanisms. Using surface energies for clean and alkylamine-passivated CdSe surfaces reported elsewhere by Manna et al (2005 J. Phys. Chem. B 109 6183), we have compared equilibrium and metastable shapes of CdSe nanowires as a function of aspect ratio and axial orientation for different degrees of surface passivation. In general, the theoretical results support the oriented-attachment of low aspect quantum dots or nanorods, followed by coalescence to form high aspect \\langle 0001\\rangle quantum wires.
Barnard, Amanda S.; Xu, Huifang; Li, Xiaochun; Pradhan, Narayan; Peng, Xiaogang
Santilli's lie-admissible mechanics. The only option commensurate with irreversibility and nonequilibrium thermodynamics
NASA Astrophysics Data System (ADS)
Our analysis of time reversal symmetry of various dynamical equations of fluid dynamics including Boltzmann integro-differential equation reveals that in a good number of cases there are no unique methods to relegate them to the so-called irreversible category unambiguously though they neither can be grouped into the reversible category. This substantiates Professor Santilli's No Reduction Theorem [1-3] that formed a base to develop genomathematics [4]. Hence, we once again substantiate the assertion of Professor Santilli that the only option commensurate with irreversibility and nonequilibrium thermodynamics is Santilli's Lie-Admissible Mechanics.
Bhalekar, Anil A.
Microcalorimetrics studies of the thermodynamics and binding mechanism between L-tyrosinamide and aptamer.
In recent years, several high-resolution structures of aptamer complexes have shed light on the binding mode and recognition principles of aptamer complex interactions. In some cases, however, the aptamer complex binding behavior and mechanism are not clearly understood, especially with the absence of structural information. In this study, it was demonstrated that isothermal titration calorimetry (ITC) and circular dichroism (CD) were useful tools for studying the fundamental binding mechanism between a DNA aptamer and L-tyrosinamide (L-TyrNH2). To gain further insight into this behavior, thermodynamic and conformational measurements under different parameters such as salt concentration, temperature, pH value, analogue of L-TyrNH2, and metal ion were carried out. The thermodynamic signature along with the coupled CD spectral change suggest that this binding behavior is an enthalpy-driven process, and the aptamer has a conformational change from B-form to A-form. The results showed that the interaction is an induced fit binding, and the driving forces in this binding behavior may include electrostatic interactions, hydrophobic effects, hydrogen bonding, and the binding-linked protonation process. The amide group and phenolic hydroxyl group of the L-TyrNH2 play a vital role in this binding mechanism. In addition, it should be noted that Mg(2+) not only improves binding affinity but also helps change the structure of the DNA aptamer. PMID:18457441
Lin, Po-Hsun; Yen, Shih-Lun; Lin, Ming-Shen; Chang, Yung; Louis, Selva Roselin; Higuchi, Akon; Chen, Wen-Yih
Open Source Physics Curricular Material for Quantum Mechanics
NSDL National Science Digital Library
The Open Source Physics Curricular Material paper describes the interactive curricular material created as part of the Open Source Physics project for the teaching and learning of quantum mechanics. Here we focus on the measurement and time evolution of two-state superpositions in the context of bound states and spin.
Belloni, Mario; Christian, Wolfgang; Brown, Douglas
Holographic duals to poisson sigma models and noncommutative quantum mechanics
NASA Astrophysics Data System (ADS)
Poisson sigma models are a very rich class of two-dimensional theories that includes, in particular, all two-dimensional dilaton gravities. By using the Hamiltonian reduction method, we show that a Poisson sigma model (with a sufficiently well-behaving Poisson tensor) on a finite cylinder is equivalent to a noncommutative quantum mechanics for the boundary data.
Vassilevich, D. V.
New Approach to N-Body Relativistic Quantum Mechanics
In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schr�dinger equation for many-body.
Ying-Qiu Gu
The two-body quantum mechanical problem on spheres
The quantum mechanical two-body problem with a central interaction on the sphere Sn is considered. Using recent results in representation theory, an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.
Alexey V. Shchepetilov
Completeness of the Coulomb Wave Functions in Quantum Mechanics
ERIC Educational Resources Information Center
Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)
Mukunda, N.
Nonlinear nonlocal Schr�dinger equation in the context of quantum mechanics
NASA Astrophysics Data System (ADS)
The nonlinear nonlocal equation describing the evolution of a fluctuating scalar field is studied. This nonlinear system naturally produces stable static configurations as a result of its relaxation to the dissipative attractors. It is found that the structures (and their spectra) observed in the frame of the model coincide with the eigenfunctions (and eigenvalues, respectively) of the linear quantum mechanical Schr�dinger equation.
Filippov, A. E.
Elementary Quantum Mechanics in a High-Energy Process
ERIC Educational Resources Information Center
Compares two approaches to strong absorption in elementary quantum mechanics; the black sphere and a model based on the continuum theory of nuclear reactions. Examines the application to proton-antiproton interactions at low momenta and concludes that the second model is the appropriate and simplest to use. (Author/GA)
Denville, A.; And Others
a q-DEFORMATION of the Parasupersymmetric Quantum Mechanics
NASA Astrophysics Data System (ADS)
A q-deformation of the parasupersymmetric quantum mechanics of one boson and one parafermion of an arbitrary order p is constructed. The deformed commutators in the algebra generate braid-type relations which lift the degeneracy originally present in the undeformed case. The connection between the deformed algebra and a class of self-similar potentials is discussed.
Chakrabarti, R.; Jagannathan, R.
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.
Turbiner, Alexander [Institute for Theoretical and Experimental Physics, Moscow 117259 (Russian Federation); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F. (Mexico)
Quantum mechanics and faster-than-light communication: Methodological considerations
Summary��A detailed quantum-mechanical analysis of a recent proposal of faster-than-light communication through wave packet reduction\\u000a is performed. The discussion allows us to focus some methodological problems about critical investigations on physical theories.
G. C. Ghirardi; T. Weber
Quantum-mechanical theory of optomechanical Brillouin cooling
We analyze how to exploit Brillouin scattering of light from sound for the purpose of cooling optomechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.
Tomes, Matthew; Bahl, Gaurav; Carmon, Tal [Department of Electrical Engineering, University of Michigan, Ann Arbor, Michigan 48109 (United States); Marquardt, Florian [Institut fuer Theoretische Physik, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen (Germany); Max Planck Institute for the Science of Light, Guenther-Scharowsky-Strasse 1/Bau 24, D-91058 Erlangen (Germany)
Relativistic-Particle Quantum Mechanics (Applications and Approximations) II.
National Technical Information Service (NTIS)
In this lecture I hope to show that relativistic-particle quantum mechanics with direct interactions is a useful tool for building models applicable to hadron systems at intermediate energies. To do this I will first describe a class of models designed to...
F. Coester
Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics.
We established a theoretical framework in terms of the curl flux, population landscape, and coherence for non-equilibrium quantum systems at steady state, through exploring the energy and charge transport in molecular processes. The curl quantum flux plays the key role in determining transport properties and the system reaches equilibrium when flux vanishes. The novel curl quantum flux reflects the degree of non-equilibriumness and the time-irreversibility. We found an analytical expression for the quantum flux and its relationship to the environmental pumping (non-equilibriumness quantified by the voltage away from the equilibrium) and the quantum tunneling. Furthermore, we investigated another quantum signature, the coherence, quantitatively measured by the non-zero off diagonal element of the density matrix. Populations of states give the probabilities of individual states and therefore quantify the population landscape. Both curl flux and coherence depend on steady state population landscape. Besides the environment-assistance which can give dramatic enhancement of coherence and quantum flux with high voltage at a fixed tunneling strength, the quantum flux is promoted by the coherence in the regime of small tunneling while reduced by the coherence in the regime of large tunneling, due to the non-monotonic relationship between the coherence and tunneling. This is in contrast to the previously found linear relationship. For the systems coupled to bosonic (photonic and phononic) reservoirs the flux is significantly promoted at large voltage while for fermionic (electronic) reservoirs the flux reaches a saturation after a significant enhancement at large voltage due to the Pauli exclusion principle. In view of the system as a quantum heat engine, we studied the non-equilibrium thermodynamics and established the analytical connections of curl quantum flux to the transport quantities such as energy (charge) transfer efficiency, chemical reaction efficiency, energy dissipation, heat and electric currents observed in the experiments. We observed a perfect transfer efficiency in chemical reactions at high voltage (chemical potential difference). Our theoretical predicted behavior of the electric current with respect to the voltage is in good agreements with the recent experiments on electron transfer in single molecules. PMID:24985680
Zhang, Z D; Wang, J
Physics on the boundary between classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Nature's laws in the domain where relativistic effects, gravitational effects and quantum effects are all comparatively strong are far from understood. This domain is called the Planck scale. Conceivably, a theory can be constructed where the quantum nature of phenomena at such scales can be attributed to something fundamentally simpler. However, arguments that quantum mechanics cannot be explained in terms of any classical theory using only classical logic seem to be based on sound mathematical considerations: there can't be physical laws that require "conspiracy". It may therefore be surprising that there are several explicit quantum systems where these considerations apparently do not apply. In the lecture we will show several such counterexamples. These are quantum models that do have a classical origin. The most curious of these models is superstring theory. This theory is often portrayed as to underly the quantum field theory of the subatomic particles, including the "Standard Model". So now the question is asked: how can this model feature "conspiracy", and how bad is that? Is there conspiracy in the vacuum fluctuations?
't Hooft, Gerard
Quantum-mechanical coherence in cell microtubules: a realistic possibility?
We discuss the possibility of quantum-mechanical coherence in Cell MicroTubules (MT), based on recent developments in quantum physics. We focus on potential mechanisms for 'energy-loss-free' transport along the microtubules, which could be considered as realizations of Frohlich's ideas on the role of solitons for superconductivity and/or biological matter. In particular, by representing the MT arrangements as cavities, we review a novel scenario, suggested in collaboration with D.V. Nanopoulos, concerning the formation of macroscopic (or mesoscopic) quantum-coherent states, as a result of the (quantum-electromagnetic) interactions of the MT dimers with the surrounding molecules of the ordered water in the interior of the MT cylinders. We suggest specific experiments to test the above-conjectured quantum nature of the microtubular arrangements inside the cell. These experiments are similar in nature to those in atomic physics, used in the detection of the Rabi-Vacuum coupling between coherent cavity modes and atoms. Our conjecture is that a similar Rabi-Vacuum-splitting phenomenon occurs in the absorption (or emission) spectra of the MT dimers, which would constitute a manifestation of the dimer coupling with the coherent modes in the ordered-water environment (dipole quanta), which emerge due to the phenomenon of 'super-radiance'. PMID:10379540
Mavromatos, N E
Deterministic quantum evolution through modification of the hypotheses of statistical mechanics
It is claimed that for all apparatus capable of performing macroscopic measurements of microscopic systems there exist special internal states for which deterministic quantum evolution alone yields a particular macroscopic outcome rather than a superposition of macroscopically distinct outcomes. Schulman maintains that these special states are distributed uniformly (in a certain sense) among the set of all states. He postulates that in the absence of precise information on apparatus initial conditions one should give equal weight to those microstates that are consistent with the macroscopic state and are special in the sense used above. Evidence is presented for this postulate's recovering the usual quantum probabilities. This theory is fully deterministic, has no collapsing wave functions, and offers a resolution of the quantum measurement problem through a revision of the usual statistical mechanical handling of initial conditions. It requires a single wave function for the entire universe and an all-encompassing conspiracy to arrange the right sort of special wave function for each experiment. As an example Schulman considers a Stern-Gerlach apparatus that measures the z component of the spin of silver atoms that pass through it. Although Schulman does not provide physical or philosophical justification for his central hypothesis, some perspective is given by examining the notions implicit in the usual principles of thermodynamics.
Schulman, L.S.
Quantum mechanical force field for hydrogen fluoride with explicit electronic polarization.
The explicit polarization (X-Pol) theory is a fragment-based quantum chemical method that explicitly models the internal electronic polarization and intermolecular interactions of a chemical system. X-Pol theory provides a framework to construct a quantum mechanical force field, which we have extended to liquid hydrogen fluoride (HF) in this work. The parameterization, called XPHF, is built upon the same formalism introduced for the XP3P model of liquid water, which is based on the polarized molecular orbital (PMO) semiempirical quantum chemistry method and the dipole-preserving polarization consistent point charge model. We introduce a fluorine parameter set for PMO, and find good agreement for various gas-phase results of small HF clusters compared to experiments and ab initio calculations at the M06-2X/MG3S level of theory. In addition, the XPHF model shows reasonable agreement with experiments for a variety of structural and thermodynamic properties in the liquid state, including radial distribution functions, interaction energies, diffusion coefficients, and densities at various state points. PMID:24880295
Mazack, Michael J M; Gao, Jiali
Quantum mechanical force field for hydrogen fluoride with explicit electronic polarization
NASA Astrophysics Data System (ADS)
The explicit polarization (X-Pol) theory is a fragment-based quantum chemical method that explicitly models the internal electronic polarization and intermolecular interactions of a chemical system. X-Pol theory provides a framework to construct a quantum mechanical force field, which we have extended to liquid hydrogen fluoride (HF) in this work. The parameterization, called XPHF, is built upon the same formalism introduced for the XP3P model of liquid water, which is based on the polarized molecular orbital (PMO) semiempirical quantum chemistry method and the dipole-preserving polarization consistent point charge model. We introduce a fluorine parameter set for PMO, and find good agreement for various gas-phase results of small HF clusters compared to experiments and ab initio calculations at the M06-2X/MG3S level of theory. In addition, the XPHF model shows reasonable agreement with experiments for a variety of structural and thermodynamic properties in the liquid state, including radial distribution functions, interaction energies, diffusion coefficients, and densities at various state points.
Mazack, Michael J. M.; Gao, Jiali
Statistical mechanics and molecular dynamics in evaluating thermodynamic properties of biomolecular recognition.
Molecular recognition plays a central role in biochemical processes. Although well studied, understanding the mechanisms of recognition is inherently difficult due to the range of potential interactions, the molecular rearrangement associated with binding, and the time and length scales involved. Computational methods have the potential for not only complementing experiments that have been performed, but also in guiding future ones through their predictive abilities. In this review, we discuss how molecular dynamics (MD) simulations may be used in advancing our understanding of the thermodynamics that drive biomolecular recognition. We begin with a brief review of the statistical mechanics that form a basis for these methods. This is followed by a description of some of the most commonly used methods: thermodynamic pathways employing alchemical transformations and potential of mean force calculations, along with end-point calculations for free energy differences, and harmonic and quasi-harmonic analysis for entropic calculations. Finally, a few of the fundamental findings that have resulted from these methods are discussed, such as the role of configurational entropy and solvent in intermolecular interactions, along with selected results of the model system T4 lysozyme to illustrate potential and current limitations of these methods. PMID:22082669
Wereszczynski, Jeff; McCammon, J Andrew
Atomistic modeling of thermodynamic properties of Pu-Ga alloys based on the Invar mechanism
NASA Astrophysics Data System (ADS)
We present an atomistic model that accounts for a range of anomalous thermodynamic properties of the fcc ? phase of Pu-Ga alloys in terms of the Invar mechanism. Two modified embedded atom method potentials are employed to represent competing electronic states in ?-Pu, each of which has an individual configuration dependence as well as distinct interactions with gallium. Using classical Monte Carlo simulations, we compute the temperature dependence of various thermodynamic properties for different dilute gallium concentrations. The model reproduces the observed effects of excessive volume reduction along with a rapid shift in thermal expansion from negative to positive values with increasing gallium concentration. It also predicts progressive stiffening upon dilute-gallium alloying, while the calculated thermal softening is nearly independent of the gallium concentration in agreement with resonant ultrasound spectroscopy measurements in the literature. Analysis of the local structure predicted by the model indicates that the distribution of the gallium atoms is not completely random in the ? phase due to the presence of short-range order associated with the Invar mechanism. This effect is consistent with the nanoscale heterogeneity in local gallium concentration which is observed in recent extended x-ray absorption fine structure spectroscopy experiments. Implications of the Invar effect for phase stability and physical interpretations of the two states are also discussed.
Lee, Tongsik; Taylor, Christopher D.; Lawson, A. C.; Conradson, Steven D.; Chen, Shao Ping; Caro, A.; Valone, Steven M.; Baskes, Michael I.
Thermodynamic and mechanical properties of crystalline CoSb3: A molecular dynamics simulation study
NASA Astrophysics Data System (ADS)
Molecular dynamics simulations have been performed to study the fundamental thermodynamic and mechanical properties of single-crystalline skutterudite CoSb3 in the nanometric scale. The several interesting thermodynamic predictions, including linear thermal expansion coefficient, specific heat capacity, thermal conductivity, and temperature dependence of elastic constants, show excellent agreement with data available in the literature. The classic mechanical tests of uniaxial tension and compression are performed respectively at constant temperatures. The CoSb3 single-crystal exhibits nonlinear elastic response during the deformation process and the sustainable stress is very high, demonstrating its outstanding stability. An interesting phenomenon occurs at compression that the stress-strain curve undergoes a transition. The cause of the transition is an atomic reconstruction, which is observed and interpreted on the basis of interatomic interactions. Both of the failure patterns under tension and compression reveal brittleness of the material. The increasing of temperature would result in a linear degradation of the effective Young's modulus and ultimate strength, but its effect on Poisson's ratio is negligible. The results provide the groundwork for future studies of service behavior of the skutterudites-based thermoelectric devices.
Yang, Xu-Qiu; Zhai, Peng-Cheng; Liu, Li-Sheng; Zhang, Qing-Jie
Quantum Mechanical/Molecular Mechanical Simulation Study of the Mechanism of Hairpin Ribozyme Catalysis
The molecular mechanism of hairpin ribozyme catalysis is studied with molecular dynamics simulations using a combined quantum mechanical and molecular mechanical (QM/MM) potential with a recently developed semiempirical AM1/d-PhoT model for phosphoryl transfer reactions. Simulations are used to derive one- and two-dimensional potentials of mean force to examine specific reaction paths and assess the feasibility of proposed general acid and base mechanisms. Density-functional calculations of truncated active site models provide complementary insight to the simulation results. Key factors utilized by the hairpin ribozyme to enhance the rate of transphosphorylation are presented, and the roles of A38 and G8 as general acid and base catalysts are discussed. The computational results are consistent with available experimental data, provide support for a general acid/base mechanism played by functional groups on the nucleobases, and offer important insight into the ability of RNA to act as a catalyst without explicit participation by divalent metal ions.
Nam, Kwangho; Gao, Jiali; York, Darrin M.
A quantum-mechanical treatment of Szilard's engine: Implications for the entropy of information
NASA Astrophysics Data System (ADS)
We present a quantum-mechanical analysis of Szilard's famous single-molecule engine, showing that it is analogous to the double-slit experiment. We further show that the energy derived from the engine's operation is provided by the act of observing the molecule's location. The engine can be operated with no increase in physical entropy, and the second law of thermodynamics does not compel us to relate physical entropy to informational entropy. We conclude that information per se is a subjective, idealized, concept separated from the physical realm. Physical entropy depends on physical objects and physical interactions, and any entropy change owing to observations is entirely a result of the entropy created in the physical apparatus by the process of observation.
Biedenharn, L. C.; Solem, J. C.
An extended phase-space SUSY quantum mechanics
NASA Astrophysics Data System (ADS)
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N = 2) realization of extended supersymmetry algebra and discuss the vacuum energy and topology of super-potentials. Shape invariance of exactly solvable extended SUSY potentials allows us to obtain analytic expressions for the entire energy spectrum of an extended Hamiltonian with, for example, Scarf potential without ever referring to an underlying differential equation.
Ter-Kazarian, G.
Adiabatic approximation in PT-symmetric quantum mechanics
NASA Astrophysics Data System (ADS)
In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics, which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.
Guo, ZhiHua; Cao, HuaiXin; Lu, Ling
Duality and the Equivalence Principle of Quantum Mechanics
Following a suggestion by Vafa, we present a quantum-mechanical model for\\u000aS-duality symmetries observed in the quantum theories of fields, strings and\\u000abranes. Our formalism may be understood as the topological limit of Berezin's\\u000ametric quantisation of the upper half-plane H, in that the metric dependence\\u000ahas been removed. Being metric-free, our prescription makes no use of global\\u000aquantum numbers.
Jose M. ISIDRO; G. Galilei
Noncommutative unification of general relativity and quantum mechanics
We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid {gamma} given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics.
Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw [Vatican Observatory, Vatican City, V-00120 Vatican City, Rome (Italy); Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw (Poland)
Quantum mechanics and faster-than-light communication Methodological considerations
NASA Astrophysics Data System (ADS)
A critical analysis is made of proposals for faster-than-light communications schemes based on quantum mechanics concepts. The point of view taken is that no reduction in one physical system can have an instantaneous effect on another, isolated system. It is shown that the philosophical contradictions exposed by the Einstein-Podolsky Rosen can be directly transferred to an interpretation of physical events. Attention is directed toward the possibility of a photon, propagating in one direction with either circular or plane polarization, entering a nonselective laser tube. The photon originally emerged from a quantum decay process which yielded two photons traveling in opposite directions. The photon in the laser gain tube precipitates a beam which is polarized as the initiating photon. A first observer can then determine the polarization observed by a second observer (with the laser) before the signal arrives. It is concluded that the FLASH argument of Herbert (1982) therefore assumes a violation of quantum mechanical laws in order to use quantum mechanics to prove that faster-than-light communication is possible.
Ghirardi, G. C.; Weber, T.
A perspective on quantum mechanics calculations in ADMET predictions.
Understanding the molecular basis of drug action has been an important objective for pharmaceutical scientists. With the increasing speed of computers and the implementation of quantum chemistry methodologies, pharmacodynamic and pharmacokinetic problems have become more computationally tractable. Historically the former has been the focus of drug design, but within the last two decades efforts to understand the latter have increased. It takes about fifteen years and over $1 billion dollars for a drug to go from laboratory hit, through lead optimization, to final approval by the U.S. Food and Drug Administration. While the costs have increased substantially, the overall clinical success rate for a compound to emerge from clinical trials is approximately 10%. Most of the attrition rate can be traced to ADMET (absorption, distribution, metabolism, excretion, and toxicity) problems, which is a powerful impetus to study these issues at an earlier stage in drug discovery. Quantum mechanics offers pharmaceutical scientists the opportunity to investigate pharmacokinetic problems at the molecular level prior to laboratory preparation and testing. This review will provide a perspective on the use of quantum mechanics or a combination of quantum mechanics coupled with other classical methods in the pharmacokinetic phase of drug discovery. A brief overview of the essential features of theory will be discussed, and a few carefully selected examples will be given to highlight the computational methods. PMID:23675934
Bowen, J Phillip; G�ner, Osman F
Thermodynamic and mechanical stabilities of tantalum nitride Ta2N3
We perform first-principles density functional calculations on a newly discovered tantalum nitride with an orthorhombic U{sub 2}S{sub 3} structure to assess its thermodynamic and mechanical stabilities. Our random search unveils a tetragonal Ta{sub 2}N{sub 3} structure that is energetically more favorable than an orthorhombic Ta{sub 2}N{sub 3} at zero pressure. We predict that the tetragonal Ta{sub 2}N{sub 3} transforms into the orthorhombic phase above a relatively low pressure of 7.7 GPa. Single-crystal elastic constant calculations reveal that orthorhombic Ta{sub 2}N{sub 3} is mechanically unstable because of a negative c{sub 66}. Our calculations suggest that minor oxygen substitution for nitrogen plays an important role in stabilizing the orthorhombic Ta{sub 2}N{sub 3} structure.
Jiang, Chao [Los Alamos National Laboratory; Lin, Zhijun [Los Alamos National Laboratory; Zhao, Yusheng [Los Alamos National Laboratory
Quantum gauge models without (classical) Higgs mechanism
NASA Astrophysics Data System (ADS)
We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.
D�tsch, Michael; Gracia-Bond�a, Jos� M.; Scheck, Florian; V�rilly, Joseph C.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.
Buschmann, J.E.
Entropy production and equilibration in Yang-Mills quantum mechanics
NASA Astrophysics Data System (ADS)
The Husimi distribution provides for a coarse-grained representation of the phase-space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse-grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse-grained entropy of a highly excited state. We show that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system.
Tsai, Hung-Ming; M�ller, Berndt
Entropy production and equilibration in Yang-Mills quantum mechanics.
The Husimi distribution provides for a coarse-grained representation of the phase-space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse-grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse-grained entropy of a highly excited state. We show that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system. PMID:22400515
Tsai, Hung-Ming; M�ller, Berndt
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
NASA Astrophysics Data System (ADS)
Spontaneous transitions between bound states of an atomic system, the "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations ( fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schr�dinger type and is defined on the extended space ?3?? n , where ?3 and ? n are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Gevorkyan, A. S.
Emergence of a New Quantum Mechanics by Multivalued Logic
NASA Astrophysics Data System (ADS)
Quantum Mechanics associated with new logic like Multivalued Logic and Fuzzy Logic has progressed in different ways and their applications can be found in many fields of sciences and technologies. All the concepts attached to this theory are far from the classical view. Classical mechanics can be viewed as crisp limit of a Fuzzy quantum mechanics. This leads to the following interpretation: It is the consequence of an assumption that a quantum particle "reside" in different place or in every path of the continuum of paths which collapse into a single "unique" trajectory of an observed classical motion The reality is "Fuzzy" and nonlocal not only in space but also in time. In this sense, idealised pointlike particles of classical mechanics corresponding to the ultimate sharpness of the fuzziness density emerge in a process of interaction between different parts of fuzzy wholeness. This process is viewed as a continuous process of defuzzification. It transforms a fuzzy reality into a crisp one. It is clear that the emerging crisp reality as a final step of measurements carries less of information that the underlying fuzzy reality. This means that there is an irreversible loss of information usually called "collapse of the wave function". It is not so much a "collapse" as a realization of one of the many possibilities existing within a fuzzy reality. Any measurements rearrange the fuzzy reality leading to different detection outcomes.
de Gerlicz, Claude Gaudeau; Antoine, Mathias; Bobola, Philippe; Flawisky, Nicolas; Hebras, Xavier; Mundedi, Musa
Third emission mechanism in solid-state nanocavity quantum electrodynamics.
Photonic crystal (PC) nanocavities have been receiving a great deal of attention recently because of their ability to strongly confine photons in a tiny space with a high quality factor. According to cavity quantum electrodynamics (cavity QED), such confined photons can achieve efficient interactions with excitons in semiconductors, leading to the Purcell effect in the weak coupling regime and vacuum Rabi splitting (VRS) in the strong coupling regime. These features are promising for applications such as quantum information processing, highly efficient single photon sources and ultra-low threshold lasers. In this context, the coupled system of a semiconductor quantum dot (QD) and a PC nanocavity has been intensively investigated in recent years.Although experimental reports have demonstrated such fundamental features, two anomalous phenomena have also been observed. First, photon emission from the cavity occurs even when it is significantly detuned from the QD. Second, spectral triplets are formed by additional bare-cavity lines between the VRS lines. These features cannot be explained by standard cavity QED theories and have prompted controversy regarding their physical mechanisms. In this review we describe the recent experimental and theoretical progress made in the investigation of these phenomena. Similar mechanisms will also occur in many other coupled quantum systems, and thus the findings are applicable to a wide range of fields. PMID:22885777
Yamaguchi, Makoto; Asano, Takashi; Noda, Susumu
Measurement and quasi-states in quantum mechanics
Part of the task of quantum logic is to account for the collapse of the state vector during measurement. A difficulty in this is that it is not obvious how to describe measurement quantum mechanically as the interaction of two or more systems; interacting quantum-mechanical systems do not possess states, so their states cannot collapse. This dissertation shows that component systems of a composite system possess families of state-like vectors. These are the quasi-projections of the state vector of the composite system, each associated with a family of commutable observables. Often these quasi-projections cluster so closely around a quasi-state that they are practically indistinguishable from it. A description of measurement based on quasi-projections reveals the apparent collapse of the state vector during measurement to be illusory. The continuous evolution of the state of the composite system give rise to abrupt changes in the quasi-projections which make it appear that the state has changed. The quasi-projections cease to cluster near one quasi-state, are momentarily scattered, and then cluster again near another quasi-state. The concept of quasi-projection is also used to generalize the quantum logic of Birkhoff and von Neumann in such a fashion that a proposition can always be assigned a truth value.
Harper, C.D.
Delirium Quantum Or, where I will take quantum mechanics if it will let me
NASA Astrophysics Data System (ADS)
Once again, I take advantage of the wonderfully liberal and tolerant mood Andrei Khrennikov sets at his yearly conferences by submitting a nonstandard paper for the proceedings. This pseudo-paper consists of excerpts drawn from two of my samizdats [Quantum States: What the Hell Are They? and Darwinism All the Way Down (and Probabilism All the Way Back Up)] that I think best summarize what I am aiming for on the broadest scale with my quantum foundations program. Section 1 tries to draw a picture of a physical world whose essence is ``Darwinism all the way down.'' Section 2 outlines how quantum theory should be viewed in light of that, i.e., as being an expression of probabilism (in Bruno de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes how the idea of ``identical'' quantum measurement outcomes, though sounding atomistic in character, nonetheless meshes well with a William Jamesian style ``radical pluralism.'' Sections 4 and 5 further detail how quantum theory should not be viewed so much as a ``theory of the world,'' but rather as a theory of decision-making for agents immersed within a quantum world-that is, a world in continual creation. Finally, Sections 6 and 7 attempt to sketch once again the very positive sense in which quantum theory is incomplete, but still just as complete is it can be. In total, I hope these heady speculations convey some of the excitement and potential I see for the malleable world quantum mechanics hints of.
Fuchs, Christopher A.
Nonlinear Dynamics of Turbulent Coronal Heating Mechanisms: Thermodynamics, Energy Storage and Release
NASA Astrophysics Data System (ADS)
Thermodynamics of the magnetically confined solar corona are investigated with fully compressible three-dimensional magnetohydrodynamic simulations. Coronal loops field lines' footpoints are shuffled by space-filling homogeneous photospheric motions giving rise to turbulent nonlinear dynamics. Field-aligned current sheets continuously form and dissipate depositing energy at the small-scales where the heating occurs. Previous studies show that current sheets thickness is orders of magnitude smaller than current state of the art observational resolution (~700 km). Therefore to understand coronal heating and its observed properties we need to understand the thermodynamics of such a system where energy is deposited at unresolved small-scales. We show that at observationally sub-resolution scales temperature is highly structured and non-homogeneously distributed. In this multi-thermal highly dynamical system, hotter and cooler plasma strands are found one next to the other at sub-resolution scales, and only a fraction of the coronal mass and volume gets heated at each time. The basal coronal heating described above is characterized by a limited storage of magnetic energy and numerous small releases of energy, so-called nanoflares. Reduced magnetohydrodynamic simulations show that such system stores a considerably higher magnetic energy when localized photospheric motions are applied. Its dynamics, mechanisms of subsequent release of the stored energy in micro- or larger flares, and the impact on coronal dynamics will be discussed.
Einaudi, G.; Dahlburg, R.; Rappazzo, A. F.; Velli, M. M.
A quantum mechanical polarizable force field for biomolecular interactions
We introduce a quantum mechanical polarizable force field (QMPFF) fitted solely to QM data at the MP2/aTZ(-hp) level. Atomic charge density is modeled by point-charge nuclei and floating exponentially shaped electron clouds. The functional form of interaction energy parallels quantum mechanics by including electrostatic, exchange, induction, and dispersion terms. Separate fitting of each term to the counterpart calculated from high-quality QM data ensures high transferability of QMPFF parameters to different molecular environments, as well as accurate fit to a broad range of experimental data in both gas and liquid phases. QMPFF, which is much more efficient than ab initio QM, is optimized for the accurate simulation of biomolecular systems and the design of drugs.
Donchev, A. G.; Ozrin, V. D.; Subbotin, M. V.; Tarasov, O. V.; Tarasov, V. I.
A quantum mechanical polarizable force field for biomolecular interactions.
We introduce a quantum mechanical polarizable force field (QMPFF) fitted solely to QM data at the MP2/aTZ(-hp) level. Atomic charge density is modeled by point-charge nuclei and floating exponentially shaped electron clouds. The functional form of interaction energy parallels quantum mechanics by including electrostatic, exchange, induction, and dispersion terms. Separate fitting of each term to the counterpart calculated from high-quality QM data ensures high transferability of QMPFF parameters to different molecular environments, as well as accurate fit to a broad range of experimental data in both gas and liquid phases. QMPFF, which is much more efficient than ab initio QM, is optimized for the accurate simulation of biomolecular systems and the design of drugs. PMID:15911753
Donchev, A G; Ozrin, V D; Subbotin, M V; Tarasov, O V; Tarasov, V I
The equivalence principle of quantum mechanics: Uniqueness theorem
Recently the authors showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p = {partial_derivative}{sub q}S{sub 0} and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, they looked for the special transformations leading to the free system with vanishing energy. Furthermore, they saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this letter they show that actually the principle uniquely leads to this solution. The authors also express the canonical and Schroedinger equations by means of the brackets recently introduced in the framework of N = 2 SYM. These brackets are the analogue of the Poisson brackets with the canonical variables taken as dependent.
Faraggi, A.E. [Univ. of Florida, Gainesville, FL (United States). Inst. for Fundamental Theory; Matone, M. [Univ. of Padova (Italy)
Developing and evaluating animations for teaching quantum mechanics concepts
NASA Astrophysics Data System (ADS)
In this paper, we describe animations and animated visualizations for introductory and intermediate-level quantum mechanics instruction developed at the University of St Andrews. The animations aim to help students build mental representations of quantum mechanics concepts. They focus on known areas of student difficulty and misconceptions by including animated step-by-step explanations of key points. The animations are freely available, with additional resources available to instructors. We have investigated their educational effectiveness both in terms of student attitude and performance. Questionnaires showed that students are on the whole very positive about the animations and make substantial use of them. A diagnostic survey administered to level 2 and 3 students showed that level 2 students significantly outperformed level 3 students on topics which they had investigated using the animations.
Kohnle, Antje; Douglass, Margaret; Edwards, Tom J.; Gillies, Alastair D.; Hooley, Christopher A.; Sinclair, Bruce D.
F-theory Yukawa couplings and supersymmetric quantum mechanics
NASA Astrophysics Data System (ADS)
The localized fermions on the intersection curve ? of D7-branes, are connected to a N=2 supersymmetric quantum mechanics algebra. Due to this algebra the fields obey a global U(1) symmetry. This symmetry restricts the proton decay operators and the neutrino mass terms. Particularly, we find that several proton decay operators are forbidden and the Majorana mass term is the only one allowed in the theory. A special SUSY QM algebra is studied at the end of the paper. In addition we study the impact of a non-trivial holomorphic metric perturbation on the localized solutions along each matter curve. Moreover, we study the connection of the localized solutions to an N=2 supersymmetric quantum mechanics algebra when background fluxes are turned on.
Oikonomou, V. K.
Novel symmetries in N=2 supersymmetric quantum mechanical models
NASA Astrophysics Data System (ADS)
We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X-Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory.
Malik, R. P.; Khare, Avinash
Quantum mechanical properties of graphene nano-flakes and quantum dots.
In recent years considerable attention has been given to methods for modifying and controlling the electronic and quantum mechanical properties of graphene quantum dots. However, as these types of properties are indirect consequences of the wavefunction of the material, a more efficient way of determining properties may be to engineer the wavefunction directly. One way of doing this may be via deliberate structural modifications, such as producing graphene nanostructures with specific sizes and shapes. In this paper we use quantum mechanical simulations to determine whether the wavefunction, quantified via the distribution of the highest occupied molecular orbital, has a direct and reliable relationship to the physical structure, and whether structural modifications can be useful for wavefunction engineering. We find that the wavefunction of small molecular graphene structures can be different from those of larger nanoscale counterparts, and the distribution of the highest occupied molecular orbital is strongly affected by the geometric shape (but only weakly by edge and corner terminations). This indicates that both size and shape may be more useful parameters in determining quantum mechanical and electronic properties, which should then be reasonably robust against variations in the chemical passivation or functionalisation around the circumference. PMID:22903345
Shi, Hongqing; Barnard, Amanda S; Snook, Ian K
Relationship between quantum mechanics with and without monopoles
We show that the inclusion of the monopole field in the three- and\\u000afive-dimensional spherically symmetric quantum mechanical systems, supplied by\\u000athe addition of the special centrifugal term, does not yield any change in the\\u000aradial wavefunction and in the functional dependence of the energy spectra on\\u000aquantum numbers. The only change in the spectrum is the lift of the
Levon Mardoyan; Armen Nersessian; Armen Yeranyan
Maximum-power quantum-mechanical Carnot engine
In their work [J. Phys. A: Math. Gen. 33, 4427 (2000)], Bender, Brody, and\\u000aMeister have shown by employing a two-state model of a particle confined in the\\u000aone-dimensional infinite potential well that it is possible to construct a\\u000aquantum-mechanical analog of the Carnot engine through the changes of both the\\u000awidth of the well and the quantum state in
Sumiyoshi Abe
Meshless local Petrov-Galerkin (MLPG) methods in quantum mechanics
Purpose � The purpose of this paper is to solve both eigenvalue and boundary value problems coming from the field of quantum mechanics through the application of meshless methods, particularly the one known as meshless local Petrov-Galerkin (MLPG). Design\\/methodology\\/approach � Regarding eigenvalue problems, the authors show how to apply MLPG to the time-independent Schr�dinger equation stated in three dimensions. Through
Williams L. Nicomedes; Renato C. Mesquita; Fernando J. S. Moreira
Degree of polarization and quantum-mechanical purity
NASA Astrophysics Data System (ADS)
The purity parameter is used in quantum mechanics to discriminate pure states from mixed states. We employ this concept to define a degree of polarization for general, three-dimensional, classical random electric fields. Our approach leads to a result that is identical with a recent definition obtained by a decomposition of the polarization matrix in terms of the Gell-Mann matrices. We also give an expression for this degree of polarization based on the constituent two-dimensional subsystems.
Moya-Cessa, H.; Moya-Cessa, J. R.; Landgrave, J. E. A.; Martinez-Niconoff, G.; Perz Leija, A.; Friberg, A. T.
When is a hidden variable theory compatible with quantum mechanics?
This paper is devoted to a study of some of the basic conditions which have to be satisfied by a hidden variable theory in\\u000a order that it can reproduce the quantum mechanical probabilities. Of course one such condition, which emerges from the important\\u000a theorem of Bell, is that a hidden variable theory has to be non-local. It is shown that
M D Srinivas
Supersymmetric quantum mechanics on non-commutative space
We construct a supersymmetric quantum mechanics in terms of two real supercharges on non-commutative space in arbitrary dimensions. We obtain the exact eigenspectra of the two- and three-dimensional non-commutative superoscillators. We further show that a reduction in the phase space occurs for a critical surface in the space of parameters. At this critical surface, the energy spectrum of the bosonic
Pijush K. Ghosh
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}
Turbiner, A. [Institute for Theoretical and Experimental Physics, Moscow 117259 (Russia)]|[Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F. (Mexico)
Quantum mechanics versus local realism for neutral kaon pairs
We formulate the theory of K0K0 pairs by including variables which determine when the two kaons will undergo a simultaneous jump of strangeness. This approach is a direct consequence of the EPR reality criterion when locality is also taken into account. The probabilities of observing K0K0 and KSK0 pairs at different proper times are shown to disagree with quantum mechanical
Paolo Privitera; Franco Selleri
Thermodynamic properties of cSi derived by quantum path-integral Monte Carlo simulations
Feynman path-integral Monte Carlo simulations of crystalline silicon, using the empirical potential of Stillinger and Weber, have been performed in the isothermal-isobaric ensemble. Several thermodynamic properties have been evaluated as a function of pressure and temperature. The calculated lattice parameter, heat capacity, thermal expansion coefficient, and bulk modulus show an overall agreement with the experimental data. However, the negative thermal
Jos� C. Noya; Carlos P. Herrero; Rafael Ram�rez
Quantum Mechanics in Chemistry (by Jack Simons and Jeff Nichols)
NASA Astrophysics Data System (ADS)
Topics in Physical Chemistry Series. Oxford University Press: New York, 1997. xxiii + 612 pp. Illustrations. ISBN 0-19-508200-1. $75.00. One of the problems faced by graduate-level quantum mechanics courses in chemistry is that there is often little time for studying chemical problems. Students must learn so much matrix algebra and notation that a first-semester course seems more like a math or physics course than chemistry. Another problem is the focus of most graduate texts. Excellent texts, such as those by Sakurai, and older treatments, such as Messiah and Cohen-Tannoudji, offer a comprehensive amount of mathematical rigor to go along with chemistry problems, but it seems the intended audience is hard-core theoretical or physical chemistry students. Requirements that are more general, such as reaction-path dynamics, structure and term symbols, and symmetry in quantum mechanical problems, are often left behind. Schatz and Ratner's Book Quantum Mechanics in Chemistry (Prentice Hall) is one book that fills this gap (at least for second-semester students); Simons and Nichols' new book is another, but it is a book that requires revision before it can be seriously considered.
McCallum, C. Michael
Quantum Mechanical Probabilities on a General Spacetime-Surface
NASA Astrophysics Data System (ADS)
A theoretical aspect of quantum mechanical probabilities is studied. In nonrelativistic quantum mechanics (NRQM) for a particle, Schr�dinger's wave function assigns probabilities to possible places where the particle is found on a surface (hypersurface in Newtonian spacetime) of constant time. We may then ask if quantum mechanical probabilities can be defined for an exhaustive set of exclusive outcomes of observations made on a surface on which Newtonian time is not constant. Such a question may be said to belong to the study of the role of time in NRQM in a broad sense. Specifically we investigate the theoretical possibility of a probabilistic description of (I) where and how many times the particle intersects the surface, and of (II) where and how many times the particle is found on the surface. For each case we formulate two conditions for the success of a probabilistic description. They are the classifiability condition and the no-interference condition, both of which are conditions on the propagator of the particle. For each case it is proved that the former condition does not hold and that consequently a probabilistic description is theoretically impossible either for (I) or for (II).
Yamada, N.; Takagi, S.
Novel symmetries in N=2 supersymmetric quantum mechanical models
We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X�Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory. -- Highlights: �Discrete symmetries of two completely different kinds of N=2 supersymmetric quantum mechanical models have been discussed. �The discrete symmetries provide physical realizations of Hodge duality. �The continuous symmetries provide the physical realizations of de Rham cohomological operators. �Our work sheds a new light on the meaning of the above abstract operators.
Malik, R.P., E-mail: firstname.lastname@example.com [Physics Department, BHU-Varanasi-221 005 (India); DST-CIMS, Faculty of Science, BHU-Varanasi-221 005 (India); Khare, Avinash, E-mail: firstname.lastname@example.com [Indian Institute of Science for Education and Research, Pune-411 021 (India)] [Indian Institute of Science for Education and Research, Pune-411 021 (India)
Coal chemistry for mechanical engineers: from macromolecular thermodynamics to reservoir simulation
In pilot trials and commercial scale field demonstrations of CO{sub 2} storage in coal seams, quite often unexpected problems with coal swelling around injector and reducing injection efficiency (e.g., Allison unit in the San Juan Basin, RECOPOL in Poland, Hokkaido project in Japan, etc.) can stall or even terminate the site development. To avoid the costly mistakes with the prospective site evaluation, the state of the art in reservoir modeling needs to be improved by taking into account coal properties at the macromolecular level. The current models are based on the rock mechanics, which ignores decades of experimental and theoretical studies of interaction between coal and injected fluids. A pseudopolymer approach is introduced to the modelers as a viable alternative, especially, at medium to high fluid pressures. Further, it is discussed how the thermodynamics of CO{sub 2} dissolution in the macromolecular network of the coal matrix can be incorporated into geomechanical models. 96 refs., 4 figs.
Vyacheslav Romanov [U.S. Department of Energy, Pittsburgh, PA (United States). National Energy Technology Laboratory
Coal Chemistry for Mechanical Engineers: From Macromolecular Thermodynamics to Reservoir Simulation
In pilot trials and commercial scale field demonstrations of CO2 storage in coal seams, quite often unexpected problems with coal swelling around injector and reducing injection efficiency (e.g., Allison unit in the San Juan Basin, RECOPOL in Poland, Hokkaido project in Japan, etc.) can stall or even terminate the site development. To avoid the costly mistakes with the prospective site evaluation, the state of the art in reservoir modeling needs to be improved by taking into account coal properties at the macromolecular level. The current models are based on the rock mechanics, which ignores decades of experimental and theoretical studies of interaction between coal and injected fluids. A pseudopolymer approach is introduced to the modelers as a viable alternative, especially, at medium to high fluid pressures. Further, it is discussed how the thermodynamics of CO2 dissolution in the macromolecular network of the coal matrix can be incorporated into geomechanical models.
Romanov, V.
Quantum mechanical effects on noise properties of nanoelectronic devices: application to Monte Carlo simulation
A discussion about the quantum mechanical effects on noise properties of ballistic (phase-coherent) nanoscale devices is presented. It is shown that quantum noise can be understood in terms of quantum trajectories. This interpretation provides a simple and intuitive explanation of the origin of quantum noise that can be very salutary for nanoelectronic engineers. In particular, an injection model is presented
Xavier Oriols