Momentum relaxation of a mobile impurity in a one-dimensional quantum gas

TL;DR

This paper studies how an impurity atom's momentum evolves and relaxes in a one-dimensional quantum gas, revealing different steady states depending on mass equality and interaction strength.

Contribution

It provides an explicit analysis of impurity momentum relaxation in a 1D quantum gas, highlighting the effects of mass ratio and interaction on steady states.

Findings

Impurity relaxes to a non-zero steady momentum $p_$.

Mass equality causes resonant scattering effects.

Explicit $p_(p_0)$ in the limit of vanishing interaction.

Abstract

We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks-Girardeau gas. We establish that given an initial momentum $p_0$ the impurity relaxes to a steady state with a non-vanishing momentum $p_\infty.$ The nature of the steady state is found to depend drastically on whether the masses of the impurity and the host are equal or not. This is due to multiple coherent scattering processes leading to a resonant interaction between the impurity and the host in the case of equal masses. The dependence of $p_\infty$ on $p_0$ remains non-trivial even in the limit of vanishing interaction between the impurity and host particles. In this limit $p_\infty(p_0)$ is found explicitly.