Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas

TL;DR

This paper rigorously derives the effective polaron dynamics for an impurity in a Fermi gas, showing that it can be approximated by a Fröhlich-type Hamiltonian and a coupled coherent state, applicable to various interaction strengths.

Contribution

The work provides a rigorous derivation of the effective polaron Hamiltonian and its approximation by a coupled coherent state for a Fermi gas impurity system.

Findings

Effective dynamics generated by a Fröhlich-type polaron Hamiltonian.

Approximation of the dynamics by an explicit coupled coherent state.

Applicable to a range of interaction couplings and time scales.

Abstract

We study the quantum dynamics of a homogeneous ideal Fermi gas coupled to an impurity particle on a three-dimensional box with periodic boundary condition. For large Fermi momentum $k_\text{F}$, we prove that the effective dynamics is generated by a Fr\"ohlich-type polaron Hamiltonian, which linearly couples the impurity particle to an almost-bosonic excitation field. Moreover, we prove that the effective dynamics can be approximated by an explicit coupled coherent state. Our method is applicable to a range of interaction couplings, in particular including interaction couplings of order 1 and time scales of the order $k_\text{F}^{-1}$.