  We investigate Landau damping of Bogoliubov excitations in a dilute Bose gas
moving in an optical lattice at finite temperatures. Using a 1D tight-binding
model, we explicitly obtain the Landau damping rate, the sign of which
determines the stability of the condensate. We find that the sign changes at a
certain condensate velocity, which is exactly the same as the critical velocity
determined by the Landau criterion of superfluidity. This coincidence of the
critical velocities reveals the microscopic mechanism of the Landau
instability. This instability mechanism is also consistent with the recent
experiment suggesting that a thermal cloud plays a crucial role in breakdown of
superfluids, since the thermal cloud is also vital in the Landau damping
process. We also examine the possibility of simultaneous disappearance of all
damping processes.
