Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

TL;DR

This paper investigates the nonequilibrium dynamics of an impurity in a Fermi sea, revealing superdiffusive behavior in higher dimensions and a temperature-dependent crossover to diffusion.

Contribution

It provides a theoretical analysis of impurity motion in a Fermi sea, showing superdiffusive behavior and temperature-dependent crossover, extending understanding of quantum impurity dynamics.

Findings

Impurity exhibits superdiffusive motion with distance ∼ t^{d/(d+1)} in d≥2.

At nonzero temperature, motion crosses over to diffusion with diffusivity D∼T^{-(d-1)/2}.

Results applicable to dilute, nondegenerate impurity concentrations.

Abstract

We treat the nonequilibrium motion of a single impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as $\sim t^{d/(d+1)}$ for the $d$-dimensional system with $d\geq 2$. For nonzero temperature $T$, this crosses over to diffusive motion at long times with diffusivity $D\sim T^{-(d-1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.