HYDRODYNAMIC DAMPING IN TRAPPED BOSE-GASES

Griffin, Wu and Stringari have derived the hydrodynamic equations of a trapped dilute Bose gas above the Bose-Einstein transition temperatur e. We give the extension which includes hydrodynamic damping, followin g the classic work of Uehling and Uhlenbeck based on the Chapman-Ensko g procedure. Our final result is a closed equation for the velocity fl uctuations delta v which includes the hydrodynamic damping due to the shear viscosity eta and the thermal conductivity kappa. Following Kavo ulakis, Pethick and Smith, we introduce a spatial cutoff in our linear ized equations when the density is so low that the hydrodynamic descri ption breaks down. Explicit expressions are given for eta and kappa, w hich are position-dependent through dependence on the local fugacity w hen one includes the effect of quantum degeneracy of the trapped gas. We also discuss a trapped Bose-condensed gas, generalizing the work of Zaremba, Griffin and Nikuni to include hydrodynamic damping due to th e (non-condensate) normal fluid.