Dynamics of trapped Bose gases at finite temperatures

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 $\omega {\tau }_{\mu }\ll 1$, where ${\tau }_{\mu }$ 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.

arXiv comment54 pages, revtex, 6 postscript figures, final version accepted for publication in Journ. Low Temp. Physics

Cited by in corpus (9)

• Cold and Ultracold Molecules: Science, Technology, and Applications
• Boltzmann-type collision operators for Bogoliubov excitations of Bose-Einstein condensates: A unified framework
• Kinetic equations for Bose-Einstein condensates from the 2PI effective action
• Quantum spirals
• Number-Conserving Approaches for Atomic Bose-Einstein Condensates: An Overview
• Time-dependent condensate fraction in an analytical model
• Stochastic motion of finite-size immiscible impurities in a dilute quantum fluid at finite temperature
• Layered Chaos in Mean-field and Quantum Many-body Dynamics
• Dissipative superfluid hydrodynamics for the unitary Fermi gas