# Kinetic theory of dark solitons with tunable friction

## TL;DR

This paper investigates how tunable friction affects the dynamics of dark solitons in a Bose-Einstein condensate coupled to a Fermi gas, revealing conditions where friction vanishes and unique negative mass behavior.

## Contribution

It introduces a controllable friction mechanism for dark solitons via impurity scattering and develops a theory for their stochastic dynamics, highlighting differences from positive mass particles.

## Key findings

- Friction coefficient depends periodically on interaction strength ratio.
- Friction can be tuned to zero, enabling frictionless soliton motion.
- Negative mass solitons do not exhibit Brownian motion without friction.

## Abstract

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a non-interacting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semi-classical dynamics of the dark soliton, a particle-like object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative mass objects and find that their dynamics are drastically different from their positive mass counterparts - they do not undergo Brownian motion. From the exact phase space probability distribution function (i.e. in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can only undergo Brownian motion in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock, et. al. (PNAS, 2017) in a similar system with bosonic impurity scatterers.