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Critical Velocity in a Bose Gas in a Moving Optical Lattice at Finite Temperatures

We study the critical velocity of a Bose-condensed gas in a moving one-dimensional (1D) optical lattice potential at finite temperatures. Solving the Gross-Pitaeavskii equation and the Bogoliubov equations, within the Popov approximation, we calculate the Bogoliubov excitations with varying lattice velocity. From the condition of the negative excitation energy, we determine the critical velocity as a function of the lattice depth and the temperature. We find that the critical velocity decreases rapidly with increasing the temperature; this result is consistent with the experimental observations. Moreover, the critical velocity shows a rapid decrease with increasing lattice depth. This tendency is much more significant than in the previous works ignoring the effect of thermal excitations in the radial direction.