Towards a kinetic theory of a dark soliton gas in one-dimensional superfluids

TL;DR

This paper develops a kinetic theory for dark soliton gases in one-dimensional superfluids, providing a new framework to understand turbulence and collective dynamics in such quantum systems.

Contribution

It introduces a novel phase-space kinetic equation for dark soliton gases, analogous to the Vlasov equation, capturing their dynamical features and collective excitations.

Findings

The kinetic theory reproduces soliton gas dynamics.

An acoustic mode is identified and verified through simulations.

The framework advances understanding of turbulence in low-dimensional superfluids.

Abstract

Soliton hydrodynamics is an appealing tool to describe strong turbulence in low-dimensional systems. Strong turbulence in quasi-one dimensional spuerfluids, such as Bose-Einstein condensates, involves the dynamics of dark solitons and, therefore, the description of a statistical ensemble of dark-solitons, i.e. soliton gases, is necessary. In this work, we propose a phase-space (kinetic) description of dark-soliton gases, introducing a kinetic equation that is formally similar to the Vlasov equation in plasma physics. We show that the proposed kinetic theory can capture the dynamical features of soliton gases and show that it sustains an acoustic mode, a fact that we corroborate with the help of direct numerical simulations. Our findings motivate the investigation of the microscopic structure of out-of-equilibrium and turbulent regimes in low-dimensional superfluids.