Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap

This paper is devoted to the study of the dynamics of two weakly coupled Bose-Einstein condensates confined in a double-well trap and perturbed by random external forces. The energy diffusion due to random forcing is quantitatively analyzed. The energy distribution is shown to evolve to a stationary distribution which depends on the initial state of the condensate only through the total number of atoms. This loss of memory of the initial conditions allows a simple and complete description of the stationary dynamics of the condensate. In particular, when the number of atoms exceeds a threshold value, the condensate temporarily localizes into one of the wells and jumps into the other well according to a Markovian dynamics. This localization occurs even in the presence of dissipation.