Nondiffusive phase spreading of a Bose-Einstein condensate at finite temperature

We show that the phase of a condensate in a finite temperature gas spreads linearly in time at long times rather than in a diffusive way. This result is supported by classical field simulations, and analytical calculations which are generalized to the quantum case under the assumption of quantum ergodicity in the system. This superdiffusive behavior is intimately related to conservation of energy during the free evolution of the system and to fluctuations of energy in the prepared initial state.