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**UNC-CH Physics and Astronomy Dissertation Defense**

Chris Shill

**“Stochastic and Semi-Classical Approaches to the Quantum Virial Expansion”**

Ultracold atomic gas experiments have seen rapid development in recent years. This is largely due to the highly clean and malleable nature of these systems that has led to such advancements as the measurement of Bose-Einstein condensate, and the development of graphene, both of which resulted in a Nobel Prize. In addition, ultracold atomic systems are, in general, dilute and dominated by short-range, s-wave interactions, which provides a perfect basis for applying stochastic methods for computing in this area of quantum matter. In particular, we focus on regions of high temperature where statistical methods, like Quantum Monte Carlo, tend to struggle. This region is known as the virial region and is described using the virial expansion of the grand thermodynamic potential.

In this talk, we will present two novel, non-perturbative techniques used for computing coefficients of the quantum virial expansion for non-relativistic Fermi gases with zero-range interactions. The first is a stochastic method that utilizes a Fourier projection to extract the virial coefficients directly from the grand potential, and the second is a semi-classical lattice approximation. We present our results for the interaction dependence on the virial coefficients in one, two, and three dimensions, as well as an estimate for the radius of convergence of the virial expansion in one dimension, a new result also provided by the Fourier projection method.