Classical fields approximation for cold weakly interacting bosons without free parameters

Classical fields approximation to cold weakly interacting bosons allows for a unified treatment of condensed and uncondensed parts of the system. Until now, however, the quantitative predictions were limited by a dependence of the results on a grid chosen for numerical implementation of the method. In this paper we propose replacing this unphysical ambiguity by an additional postulate: the temperature of the gas at thermal equilibrium should be the same as that of an ideal Bose gas with the same fraction of condensed atoms. As it turns-out, with this additional assumption, nearly all atoms are within the classical fields, thus the method applies to the whole system

Superfluidity of the BEC at finite temperature

We use the classical fields approximation to study a translational flow of the condensate with respect to the thermal cloud in a weakly interacting Bose gas. We study both, subcritical and supercritical relative velocity cases and analyze in detail a state of stationary flow which is reached in the dynamics. This state corresponds to the thermal equilibrium, which is characterized by the relative velocity of the condensate and the thermal cloud. The superfluidity manifests itself in the existence of many thermal equilibria varying in (the value of this velocity) the relative velocity between the condensate and the thermal cloud. We pay a particular attention to excitation spectra in a phonon as well as in a particle regime. Finally, we introduce a measure of the amount of the superfluid fraction in a weakly interacting Bose gas, allowing for the precise distinction between the superfluid and the condensed fractions in a single and consistent framework.Comment: 8 pages, 5 figure