Landau instability and mobility edges of the interacting one-dimensional Bose gas in weak random potentials

TL;DR

This paper investigates how weak random potentials affect the superfluidity and localization of an interacting 1D Bose gas, revealing the role of Landau instability and mobility edges in these phenomena.

Contribution

It provides a quantitative analysis of Landau instability and demonstrates the existence of effective mobility edges in an interacting 1D Bose gas with weak disorder.

Findings

Interactions suppress frictional force and inhibit Anderson localization.

Landau instability is characterized using the dynamic structure factor.

Effective mobility edges are identified in the system.

Abstract

We study the frictional force exerted on the trapped, interacting 1D Bose gas under the influence of a moving random potential. Specifically we consider weak potentials generated by optical speckle patterns with finite correlation length. We show that repulsive interactions between bosons lead to a superfluid response and suppression of frictional force, which can inhibit the onset of Anderson localisation. We perform a quantitative analysis of the Landau instability based on the dynamic structure factor of the integrable Lieb-Liniger model and demonstrate the existence of effective mobility edges.