A many-fermion generalization of the Caldeira-Leggett model

TL;DR

This paper extends the Caldeira-Leggett model to many fermions in a harmonic trap, analyzing their Green's functions and relaxation dynamics under dissipation using bosonization.

Contribution

It introduces a many-fermion generalization of the Caldeira-Leggett model and explores its effects on fermionic Green's functions and thermalization processes.

Findings

Calculation of one- and two-particle Green's functions

Analysis of relaxation and dephasing of added particles

Discussion of bath-induced effective interactions

Abstract

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a dissipative environment: The fermions are subject to a fluctuating force deriving from a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate one- and two-particle Green's functions of the fermions. We discuss the relaxation of a single extra particle added above the Fermi sea, considering also dephasing of a particle added in a coherent superposition of states. The consequences of the separation of center-of-mass and relative motion, the Pauli principle, and the bath-induced effective interaction are discussed. Finally, we extend our analysis to a more generic coupling between system and bath, that results in complete thermalization of the system.