Toward the Quantum Thermodynamics Computational Engine

Systems of numerous interacting particles are present throughout nature, from composing everyday metals to forming neutron stars. A quantum mechanical understanding of them is therefore desirable, since it could lead to discoveries of new materials and technologies, to further understanding of the origin of the universe, and more. Such an understanding is notoriously difficult, especially in the case where systems are strongly interacting, and this challenge is known as the quantum many-body problem. Given its ubiquity and vast interest, many approaches to tackle the quantum many-body problem have been developed. These generally fall into two extreme categories: analytic and numeric. In this dissertation, we investigate methods from each, namely the analytic virial expansion and the numerical quantum Monte Carlo. Based on our studies, we develop a novel approach using automated algebra, which bridges the two categories by programming computers to handle the analytic calculations. This approach was first used by our group in the context of the virial expansion. We build upon the success of this approach by developing a program, called the Quantum Thermodynamics Computational Engine (QTCE), that goes beyond the virial expansion and aims to access systems at low temperature and high density, which are relevant for ultracold atomic gases and neutron matter. Several intermediate chapters present projects leading to the QTCE, together with their corresponding results and associated publications.