Title: Fermions in Two Dimensions: Scattering and Many-Body Properties,
Abstract: Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly
popular topic of research. The interaction strength between spin-up and
spin-down particles in two-component Fermi gases can be tuned in experiments,
allowing for a strongly interacting regime where the gas properties are yet to
be fully understood. We have probed this regime for 2D Fermi gases by
performing T=0 ab initio diffusion Monte Carlo calculations. The many-body
dynamics are largely dependent on the two-body interactions, therefore we start
with an in-depth look at scattering theory in 2D. We show the partial-wave
expansion and its relation to the scattering length and effective range. Then
we discuss our numerical methods for determining these scattering parameters.
We close out this discussion by illustrating the details of bound states in 2D.
Transitioning to the many-body system, we use variationally optimized wave
functions to calculate ground-state properties of the gas over a range of
interaction strengths. We show results for the energy per particle and
parametrize an equation of state. We then proceed to determine the chemical
potential for the strongly interacting gas.