Dynamics of trapped Bose gases at finite temperatures

E. Zaremba; T. Nikuni; A. Griffin

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arXiv · cond-mat/9903029

Dynamics of trapped Bose gases at finite temperatures

E. Zaremba·T. Nikuni·A. Griffin

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Abstract

Starting from an approximate microscopic model of a trapped Bose-condensed gas at finite temperatures, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the excited atoms. The kinetic equation includes collisions between the condensate and non-condensate atoms ($C_{12}$), in addition to collisions between the excited atoms as described by the Uehling-Uhlenbeck ($C_{22}$) collision integral. Assuming that the $C_{22}$ collision rate is sufficiently rapid to produce a local equilibrium Bose distribution, the kinetic equation can be used to derive hydrodynamic equations for the non-condensate. These equations include a description of the equilibration of the local chemical potentials of the condensate and non-condensate components which gives rise to a new relaxational mode associated with the exchange of atoms between the two components. We show how the Landau two-fluid equations emerge in the frequency domain $ωτ_μ\ll 1$, where $τ_μ$ is a characteristic relaxation time of the equilibration process. This process provides an additional source of damping of the collective modes (first and second sound in the case of a uniform system). Our equations are consistent with the generalized Kohn theorem. Finally, a variational solution of the equations is developed which is used to determine some of the monopole, dipole and quadrupole normal modes of a trapped Bose gas in an isotropic trap.

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E. Zaremba, T. Nikuni, A. Griffin. 1999-06-15. Dynamics of trapped Bose gases at finite temperatures. https://arxiv.org/abs/cond-mat/9903029

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