Two-fluid hydrodynamics of a Bose gas including damping from normal fluid transport coefficients

We extend our recent work on the two-fluid hydrodynamics of the condensate and noncondensate in a trapped Bose gas by including the dissipation associ ated with viscosity and thermal conduction in the thermal cloud. For purpos es of illustration, we consider the hydrodynamic modes in the case of a uni form Bose gas. A finite thermal conductivity and shear viscosity give rise to a damping of the first and second sound modes, in addition to the dampin g found previously due to the lack of diffusive equilibrium between the con densate and noncondensate. The relaxational mode associated with this equil ibration process is strongly coupled to thermal fluctuations and reduces to the usual thermal diffusion mode above the Bose-Einstein transition. In co ntrast to the standard Landau two-fluid hydrodynamics, we predict a damped mode centered at zero frequency, in addition to the usual second sound doub let.