Volume 133, Number 2, January 2021
|Number of page(s)||7|
|Published online||24 March 2021|
Towards a kinetic theory of dark-soliton gases in one-dimensional superfluidsa
1 Instituto de Plasmas e Fusão Nuclear - Lisboa, Portugal
2 Instituto Superior Técnico - Lisboa, Portugal
3 Physics Department, Blackett Laboratory, Imperial College London - London UK
Received: 24 November 2020
Accepted: 11 February 2021
Soliton hydrodynamics is an appealing tool to describe strong turbulence in low-dimensional systems. Strong turbulence in quasi-one-dimensional superfluids, 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.
PACS: 03.75.Lm – Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations / 47.27.nb – Boundary layer turbulence
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