Emergent Quasi-Bosonicity in Interacting Fermi Gases

TL;DR

This thesis develops a bosonization method to analyze interacting Fermi gases, deriving bounds on correlation energy and exploring emergent quasi-bosonic behavior, including extensions to attractive potentials and plasmon states.

Contribution

It introduces a novel bosonization approach for Fermi gases that captures both bosonic and exchange contributions to correlation energy, extending understanding of quasi-bosonic phenomena.

Findings

Derived an upper bound for correlation energy including bosonic and exchange contributions.

Extended analysis to weakly attractive potentials.

Outlined the derivation of an effective Hamiltonian and plasmon states.

Abstract

This thesis concerns the correlation structure of interacting Fermi gases on a torus in the mean-field regime. A bosonization method in the spirit of Sawada is developed to analyze the system, and is applied to obtain an upper bound for the correlation energy of the system for a wide class of repulsive interaction potentials, including the Coulomb potential. This upper bound includes both a bosonic contribution, as found in the bosonic model of Sawada, and an exchange contribution, as was found by Gell-Mann and Brueckner but which was missed by Sawada's model. An extension to weakly attractive potentials is also presented, as is an outline of the derivation of an effective Hamiltonian for regular interaction potentials, and the construction of plasmon states for this outside of the mean-field setting. This thesis is based on the papers [arXiv:2106.11161, arXiv:2206.13073, arXiv:2208.01581].