Wave Kinetic Description of Superfluidity

Peter W�lfle

José Tito Mendonça

Abstract We derive a system of two coupled wave-kinetic equations for the condensate and for the thermal gas. This provides a simple and elegant model, based on a two fluid interaction, in the spirit of the traditional theory of superfluidity. One of the fluids is the condensed gas, and the other is the fluid of bogolon quasi-particles. As an illustration, we apply this wave-kinetic model to the description of the second-sound.

H. Fröhlich

Li Chêng-Chung

C. Pereira, José Tito Mendonça, João D. Rodrigues +1 more

Abstract 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.