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Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases

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Title: Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases
Author: Galea, Alexander
Department: Department of Physics
Program: Physics
Advisor: Gezerlis, Alexandros
Abstract: Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. 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 (DMC) calculations. In order to motivate our work, we first present an overview of 20th century breakthroughs relating to the discovery and understanding of quantum degeneracy and then we review the recent experimental advancements in cold atomic physics. The final topic in our introduction is a superfluid phase of nuclear matter, expected to exist in neutron stars, that can be compared to a Fermi gas of cold atoms. Following this, we describe our methods piece by piece. First we focus on the two-body problem, showing the partial wave expansion and its relation to scattering parameters for both 2D and 3D. After presenting the basics, we discuss our numerical methods for determining the scattering parameters. Solving for these allow us to define the interaction regime and guarantee diluteness of the many-body system. We build up to this many-body problem by first studying the non-interacting system with emphasis on finite size effects. The many-body wave functions we use for our QMC calculations are then introduced. These contain variational parameters and are encoded with some knowledge of the interactions. Having discussed the problem and our methods, our numerical multi-dimensional integration techniques are explained. We use variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) to calculate ground state properties of the gas over a range of interaction strengths. We determine the energy per particle, Tan's contact parameter, the chemical potential, and the pairing gap, all following from variationally optimized many-body wave functions.
Date: 2016-01
Rights: Attribution-NonCommercial-NoDerivs 2.5 Canada

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Attribution-NonCommercial-NoDerivs 2.5 Canada Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 2.5 Canada