Hydrodynamics of Superfluid Bose Gases in an Optical Lattice at Finite   Temperatures
  Starting from an effective action for the order parameter field, we derive a coupled set of generalized hydrodynamic equations for a Bose condensate in an optical lattice at finite temperatures. Using the linearized hydrodynamic equations, we study the microscopic mechanism of the Landau instability due to the collisional damping process between condensate and noncondensate atoms. It is shown that the Landau criterion of the superfluidity for the uniform system is modified due to the presence of the periodic optical lattice potential. 
Satoru Konabe and Tetsuro Nikuni