Bosonization of Fermionic Many-Body Dynamics

TL;DR

This paper rigorously demonstrates that the complex fermionic many-body dynamics in a three-dimensional Fermi gas can be effectively approximated by a bosonic evolution of particle-hole pairs, simplifying analysis of such systems.

Contribution

It introduces a rigorous approximate bosonization method for fermionic many-body dynamics in the coupled semiclassical and mean-field regime.

Findings

Fermionic dynamics approximated by bosonic evolution

Validates approximate bosonization in a rigorous framework

Applicable to collective particle-hole excitations

Abstract

We consider the quantum many-body evolution of a homogeneous Fermi gas in three dimensions in the coupled semiclassical and mean-field scaling regime. We study a class of initial data describing collective particle-hole pair excitations on the Fermi ball. Using a rigorous version of approximate bosonization, we prove that the many-body evolution can be approximated in Fock space norm by a quasifree bosonic evolution of the collective particle-hole excitations.