Instability of a superfluid Bose gas induced by a locked thermal gas in   an optical lattice
  We use a dissipative Gross-Petaevskii equation derived from the Bose-Hubbard Hamiltonian to study the effect of the thermal component on the stability of a current-carrying superfluid state of a Bose gas in an optical lattice potential. We explicitly show that the superfluid state becomes unstable at certain quasi-momentum of the condensate due to a thermal component which is locked by an optical lattice potential. It is shown that this instability coincides with the Landau instability derived from the GP equation. 
Satoru Konabe and Tetsuro Nikuni