LandauKhalatnikov twofluid hydrodynamics of a trapped Bose gas
Abstract
Starting from the quantum kinetic equation for the noncondensate atoms and the generalized GrossPitaevskii equation for the condensate, we derive the twofluid hydrodynamic equations of a trapped Bose gas at finite temperatures. We follow the standard ChapmanEnskog procedure, starting from a solution of the kinetic equation corresponding to the complete local equilibrium between the condensate and the noncondensate components. Our hydrodynamic equations are shown to reduce to a form identical to the wellknown LandauKhalatnikov twofluid equations, with hydrodynamic damping due to the deviation from local equilibrium. The deviation from local equilibrium within the thermal cloud gives rise to dissipation associated with shear viscosity and thermal conduction. In addition, we show that effects due to the deviation from the diffusive local equilibrium between the condensate and the noncondensate (recently considered by Zaremba, Nikuni, and Griffin) can be described by four frequencydependent second viscosity transport coefficients. We also derive explicit formulas for all the transport coefficients. These results are used to introduce two new characteristic relaxation times associated with hydrodynamic damping. These relaxation times give the rate at which local equilibrium is reached and hence determine whether one is in the twofluid hydrodynamic region.
 Publication:

Physical Review A
 Pub Date:
 March 2001
 DOI:
 10.1103/PhysRevA.63.033608
 arXiv:
 arXiv:condmat/0009333
 Bibcode:
 2001PhRvA..63c3608N
 Keywords:

 03.75.Fi;
 05.30.Jp;
 67.40.Db;
 Boson systems;
 Quantum statistical theory;
 ground state elementary excitations;
 Condensed Matter  Statistical Mechanics
 EPrint:
 26 pages, 3 postscript figures, submitted to PRA