Dynamics and Bloch oscillations of mobile impurities in one-dimensional quantum liquids

TL;DR

This paper investigates the motion of a mobile impurity in a one-dimensional quantum liquid, revealing how it undergoes Bloch oscillations, energy radiation, and drift, with exact results for mobility and friction derived.

Contribution

It provides the first exact analysis of Bloch oscillations and energy radiation for impurities in 1D quantum liquids, linking these phenomena to the impurity's dispersion relation.

Findings

Impurity induces a periodic dispersion relation with period 2πn.

External forces cause Bloch oscillations with energy radiation and drift.

Exact formulas for mobility and thermal friction are derived.

Abstract

We study dynamics of a mobile impurity moving in a one-dimensional quantum liquid. Such an impurity induces a strong non-linear depletion of the liquid around it. The dispersion relation of the combined object, called depleton, is a periodic function of its momentum with the period 2\pi n, where n is the mean density of the liquid. In the adiabatic approximation a constant external force acting on the impurity leads to the Bloch oscillations of the impurity around a fixed position. Dynamically such oscillations are accompanied by the radiation of energy in the form of phonons. The ensuing energy loss results in the uniform drift of the oscillation center. We derive exact results for the radiation-induced mobility as well as the thermal friction force in terms of the equilibrium dispersion relation of the dressed impurity (depleton). These results show that there is a wide range of external forces where the (drifted) Bloch oscillations exist and may be observed experimentally.