A continuum path integral approach to the simulation of a unitary gas

Knapp, Adam Christopher

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https://hdl.handle.net/2142/88132 Copy

Description

Title

A continuum path integral approach to the simulation of a unitary gas

Author(s)

Knapp, Adam Christopher

Issue Date

2015-04-29

Director of Research (if dissertation) or Advisor (if thesis)

Ceperley, David M.

Doctoral Committee Chair(s)

Ceperley, David M.

Committee Member(s)

• Clark, Bryan K
• Gruebele, Martin
• Phillips, Philip W.

Department of Study

Chemistry

Discipline

Chemical Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Unitary Fermi Gas
• Computational Simulation of Cold Atoms

Abstract

This thesis presents an investigation by simulation of a unpolarized fermionic unitary gas system composed of two interacting fermionic species. While these species do not interact amongst themselves, they interact with each other using a pairwise zero-range delta function potential that has been tuned to unitarity i.e.the scattering length $a_{s}=-\infty$. A path integral Monte Carlo simulation of such a system is performed using an exact novel zero-range, delta function pair propagator which has been tuned to the unitary limit so that essentially all interactions amongst the interacting particles are comprised of s-wave interactions. This tuning in some sense yields the simplest imaginable interacting fermionic system which out to display features that would apply universally to interacting fermionic particles with particular interest within this field of study being in understanding the unitary BCS-BEC crossover. Numerical and ergodic challenges to sampling a divergent approximate path integral are discussed and solutions are proposed, implemented and explored. This thesis represents a step closer to this understanding by investigating this system with this novel propagator in a fixed-node path integral Monte Carlo framework and comparing to earlier work.

Graduation Semester

2015-8

Type of Resource

text

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http://hdl.handle.net/2142/88132

Copyright and License Information

Copyright 2015 Adam Christopher Knapp

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