Kinetic Properties of a Bose-Einstein Gas at Finite Temperature

Abstract

We study, in the framework of the Boltzmann-Nordheim equation (BNE), the kinetic properties of a boson gas above the Bose-Einstein transition temperature $T_c$. The BNE is solved numerically within a new algorithm, that has been tested with exact analytical results for the collision rate of an homogeneous system in thermal equilibrium. In the classical regime ($T>6T_c$), the relaxation time of a quadrupolar deformation in momentum space is proportional to the mean free collision time ${\tau }_{relax}\sim T^{-1/2}$. Approaching the critical temperature ($T_c<T<2.7T_c$), quantum statistic effects in BNE become dominant, and the collision rate increases dramatically. Nevertheless, this does not affect the relaxation properties of the gas that depend only on the spontaneous collision term in BNE. The relaxation time ${\tau }_{relax}$ is proportional to $(T-T_c{)}^{-1/2}$, exhibiting a critical slowing down. These phenomena can be experimentally confirmed looking at the damping properties of collective motions induced on trapped atoms. The possibility to observe a transition from collisionless (zero-sound) to hydrodynamic (first-sound) is finally discussed.

RevTeX, 5 figures. Submitted to Phys. Rev. A

References in corpus (9)

• Collective excitations of a trapped Bose-condensed gas
• Ground-State Properties of Magnetically Trapped Bose-Condensed Rubidium Gas
• Evolution of a Bose-condensed gas under variations of the confining potential
• Collective excitations of atomic Bose-Einstein condensates
• Condensate fraction and critical temperature of a trapped interacting Bose gas
• Kinetics of Bose-Condensation
• Quantum Kinetic Theory I: A Quantum Kinetic Master Equation for Condensation of a weakly interacting Bose gas without a trapping potential
• Quantum Kinetic Theory III: Simulation of the Quantum Boltzmann Master Equation
• Quantum saturation and condensation of excitons in Cu${}_2$O: a theoretical study

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• Sympathetic cooling of an atomic Bose-Fermi gas mixture
• Cross-Dimensional relaxation in Bose-Fermi mixtures
• Damping and revivals of collective oscillations in a finite-temperature model of trapped Bose-Einstein condensation
• High temperature superconductivity due to the long-range electron-phonon interaction, application to isotope effects, thermomagnetic transport and nanoscale heterogeneity in cuprates
• Explicit finite-difference and direct-simulation-MonteCarlo method for the dynamics of mixed Bose-condensate and cold-atom clouds