We investigate Landau damping of Bogoliubov excitations in a dilute Bose gasmoving in an optical lattice at finite temperatures. Using a 1D tight-bindingmodel, we explicitly obtain the Landau damping rate, the sign of whichdetermines the stability of the condensate. We find that the sign changes at acertain condensate velocity, which is exactly the same as the critical velocitydetermined by the Landau criterion of superfluidity. This coincidence of thecritical velocities reveals the microscopic mechanism of the Landauinstability. This instability mechanism is also consistent with the recentexperiment suggesting that a thermal cloud plays a crucial role in breakdown ofsuperfluids, since the thermal cloud is also vital in the Landau dampingprocess. We also examine the possibility of simultaneous disappearance of alldamping processes.
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