Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: an example of an anti-damped Josephson junction

TL;DR

This paper investigates the finite-temperature dynamics of matter-wave dark solitons in Bose-Einstein condensates influenced by linear and periodic potentials, modeling an anti-damped Josephson junction through a dissipative Gross-Pitaevskii equation.

Contribution

It introduces an analytical reduced model for dark soliton dynamics at finite temperatures, incorporating an effective washboard potential and anti-damping, linking soliton behavior to Josephson junction physics.

Findings

Good agreement with Bogoliubov-de Gennes analysis for small wavenumbers

Analytical model captures key dynamics of dark solitons at finite temperature

Qualitative analysis reveals stability and motion characteristics

Abstract

We study matter-wave dark solitons in atomic Bose-Einstein condensates at finite temperatures, under the effect of linear and periodic potentials. Our model, namely a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark soliton perturbation theory, which results in a Newtonian equation of motion for the dark soliton center. This reduced model, which incorporates an effective washboard potential and an anti-damping term, constitutes an example of an anti-damped Josephson junction. We present a qualitative (local and global) analysis of the equation of motion. For sufficiently small wavenumbers of the periodic potential and weak linear potentials, the results are found to be in good agreement with pertinent ones obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.