Superfluidity of the BEC at finite temperature.

Faculty of Mathematics and Sciences, Cardinal Stefan Wyszyn´ski University, Warsaw, Poland(Dated: February 2, 2008)We use the classical fields approximation to study a translational flow of the condensate withrespect to the thermal cloud in a weakly interacting Bose gas. We study both, subcritical andsupercritical relative velocity cases and analyze in detail a state of stationary flow which is reachedin the dynamics. This state corresponds to the thermal equilibrium, which is characterized by therelative velocity of the condensate and the thermal cloud. The superfluidity manifests itself in theexistence of many thermal equilibria varying in (the value of this velocity) the relative velocitybetween the condensate and the thermal cloud. We pay a particular attention to excitation spectrain a phonon as well as in a particle regime. Finally, we introduce a measure of the amount of thesuperfluid fraction in a weakly interacting Bose gas, allowing for the precise distinction between thesuperfluid and the condensed fractions in a single and consistent framework.