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Journal of Physics A Mathematical and Theoretical

Wave-kinetic description of finite temperature Bose–Einstein condensates

José Tito Mendonça

Published May 31, 2016• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1751-8113/49/27/275501

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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.
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Superfluid 4^44He at a finite temperature is described by the two-fluid model with the normal fluid component and the superfluid component.We formulate the two-fluid model for two-component BECs, namely two-superfluid model, starting from the coupled Gross-Pitaevskii equations.The two-superfluid model well corresponds to the two-fluid model in superfluid 4^44He.In a special condition, the two sound modes in the two-superfluid model behave like first and second sounds in the two-fluid model of superfluid 4^44He.
We give an overview of the current theory of collective modes in trapped atomic gases at finite temperatures, when the dynamics of the condensate and non-condensate must both be considered. A simple introduction is given to the quantum field formulation of the dynamics of an interacting Bose-condensed system, based on equations of motion for the condensate wavefunction and single-particle Green's functions for the non-condensate atoms. We discuss the nature of excitations in the mean-field collisionless region, including the Beliaev second-order approximation for the self-energies. We also sketch the derivation of coupled two-fluid hydrodynamic equations using a simple kinetic equation which includes collisions between condensate and non-condensate atoms.
Abstract We consider the nonlinear coupling between an exact vortex solution in a Bose–Einstein condensate and a spectrum of elementary excitations in the medium. These excitations, or Bogoliubov–de Gennes modes, are indeed a special kind of phonons. We treat the spectrum of elementary excitations in the medium as a gas of quantum particles, sometimes also called bogolons . An exact kinetic equation for the bogolon gas is derived, and an approximate form of this equation, valid in the quasi-classical limit, is also obtained. We study the energy transfer between the vortex and the bogolon gas, and establish conditions for vortex instability and damping.
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We derive coupled equations of motion for the condensate (superfluid) and noncondensate (normal fluid) degrees of freedom in a trapped Bose gas at finite temperatures. Our results are based on the Hartree-Fock-Popov approximation for the time-dependent condensate wave function, and thermodynamic local equilibrium for the noncondensate atoms. In the special case of a uniform weakly interacting gas, our hydrodynamic equations are shown to be consistent with the two-fluid equations of Landau. The collective modes in a parabolically trapped Bose gas include the analog of the out-of-phase second-sound mode in superfluid 4He{}^{4}\mathrm{He}4He.