Propagation of a Dark Soliton in a Disordered Bose-Einstein Condensate

TL;DR

This paper investigates how a dark soliton propagates through a disordered Bose-Einstein condensate, revealing algebraic decay over a characteristic length unaffected by initial velocity, with implications for understanding nonlinear wave dynamics in disordered quantum systems.

Contribution

It introduces a well-defined analysis of dark soliton decay in a disordered BEC, highlighting algebraic decay and independence from initial velocity, expanding understanding of nonlinear disordered systems.

Findings

Dark soliton decays algebraically in disordered BEC

Decay length is independent of initial velocity

Characteristic decay time is determined

Abstract

We consider the propagation of a dark soliton in a quasi 1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.