Matter-wave dark solitons: stochastic vs. analytical results

TL;DR

This paper compares stochastic and analytical models of matter-wave dark solitons in atomic condensates at finite temperatures, highlighting fluctuation effects and the effectiveness of simplified equations in capturing average dynamics.

Contribution

It demonstrates the agreement between stochastic simulations, dissipative models, and analytical perturbation theory in describing soliton behavior at finite temperatures.

Findings

Stochastic simulations show observable trajectory fluctuations.

Averaged dynamics follow temperature-dependent growth in oscillation amplitude.

Simplified dissipative equations accurately predict average soliton motion.

Abstract

The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual soliton trajectories, attributed to inherent fluctuations in both phase and density of the underlying medium. Averaging over a number of such trajectories (as done in experiments) washes out such background fluctuations, revealing a well-defined temperature-dependent temporal growth in the oscillation amplitude. The average soliton dynamics is well captured by the simpler dissipative Gross-Pitaevskii equation, both numerically and via an analytically-derived equation for the soliton center based on perturbation theory for dark solitons.