Critical velocity of a mobile impurity in one-dimensional quantum liquids

TL;DR

This paper investigates the critical velocity of a mobile impurity in one-dimensional quantum liquids, revealing a mass-dependent transition in impurity dynamics that affects superfluid behavior and leads to non-analytic velocity responses.

Contribution

It introduces a theoretical framework showing how impurity mass influences dispersion and dynamics, leading to a critical mass threshold and novel velocity phenomena in 1D quantum liquids.

Findings

Heavy impurities with mass exceeding a critical value develop metastable dispersion branches.

Impurities above the critical mass exhibit abrupt velocity changes and energy loss.

The impurity drift velocity shows non-analytic dependence on small external forces.

Abstract

We study the notion of superfluid critical velocity in one spatial dimension. It is shown that for heavy impurities with mass $M$ exceeding a critical mass $M_\mathrm{c}$, the dispersion develops periodic metastable branches resulting in dramatic changes of dynamics in the presence of an external driving force. In contrast to smooth Bloch Oscillations for $M<M_\mathrm{c}$, a heavy impurity climbs metastable branches until it reaches a branch termination point or undergoes a random tunneling event, both leading to an abrupt change in velocity and an energy loss. This is predicted to lead to a non-analytic dependence of the impurity drift velocity on small forces.