Josephson oscillations of two weakly coupled Bose-Einstein condensates

A numerical experiment based on a particle number-conserving quantum field theory is performed for two initially independent Bose-Einstein condensates that are coherently coupled at two temperatures. The present model illustrates ab initio that the initial relative phase of each of the two condensates doesn't remain random, but is distributed around integer multiple values of $2\pi$ from the interference and thermalization of forward and backward propagating matter waves at the Boltzmann equilibrium, that intrinsically measures zero average phases for each of the two independent condensates. Following this approach, focus is put on the original Gedanken experiment of Anderson on whether a Josephson current between two initially separated Bose-Einstein condensates occurs in a deterministic way or not, depending on the initial phase distribution.