# Quantum mean-field asymptotics and multiscale analysis

```@article{Ammari2017QuantumMA,
title={Quantum mean-field asymptotics and multiscale analysis},
author={Zied Ammari and S{\'e}bastien Breteaux and Francis Nier},
journal={Tunisian Journal of Mathematics},
year={2017}
}```
• Published 23 January 2017
• Physics, Mathematics
• Tunisian Journal of Mathematics
We study, via multiscale analysis, some defect of compactness phenomena which occur in bosonic and fermionic quantum mean-field problems. The approach relies on a combination of mean-field asymptotics and second microlocalized semiclassical measures. The phase space geometric description is illustrated by various examples.
8 Citations
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• Mathematics
Communications in Contemporary Mathematics
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In this paper, we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, we provide
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This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case
• Mathematics
Nonlinearity
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In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent
In this paper we study the semiclassical behavior of quantum states acting on the C*-algebra of canonical commutation relations, from a general perspective. The aim is to provide a unified and
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• Mathematics, Physics
Journal of Spectral Theory
• 2019
We study the quasi-classical limit of the Pauli-Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field. We trace out the
In this paper we study the semiclassical behavior of quantum states acting on the C*-algebra of canonical commutation relations, from a general perspective. The aim is to provide a unified and
• Physics
• 2008
Abstract.This article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these
— This article is devoted to some singularly perturbed semi-classical asymptotics. It corresponds to a critical case where standard semi-classical techniques do not apply any more. We show how the
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We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions.
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Abstract:We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) space-times. We develop a purely local version of the
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The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems.
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We consider the time evolution of a system of N identical bosons whose interaction potential is rescaled by N−1. We choose the initial wave function to describe a condensate in which all particles
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Introduction 1. Local symplectic geometry 2. The WKB-method 3. The WKB-method for a potential minimum 4. Self-adjoint operators 5. The method of stationary phase 6. Tunnel effect and interaction
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