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.