Free time evolution of a tracer particle coupled to a Fermi gas in the high-density limit

TL;DR

This paper investigates the long-time behavior of a tracer particle in a dense Fermi gas, showing that its dynamics can be approximated by a mean field model despite large potential fluctuations.

Contribution

It demonstrates that in a dense Fermi gas, the tracer particle's dynamics closely follow an effective free evolution with a mean field shift, even outside the weak coupling regime.

Findings

Effective dynamics approximates the true evolution at large densities.

Mean field potential accurately describes the system despite large fluctuations.

Contrasts with bosonic gases where mean field fails quickly.

Abstract

The dynamics of a particle coupled to a dense and homogeneous ideal Fermi gas in two spatial dimensions is studied. We analyze the model for coupling parameter g=1 (i.e., not in the weak coupling regime), and prove closeness of the time evolution to an effective dynamics for large densities of the gas and for long time scales of the order of some power of the density. The effective dynamics is generated by the free Hamiltonian with a large but constant energy shift which is given at leading order by the spatially homogeneous mean field potential of the gas particles. Here, the mean field approximation turns out to be accurate although the fluctuations of the potential around its mean value can be arbitrarily large. Our result is in contrast to a dense bosonic gas in which the free motion of a tracer particle would be disturbed already on a very short time scale. The proof is based on the use of strong phase cancellations in the deviations of the microscopic dynamics from the mean field time evolution.