Anomalous phase fluctuations of a superfluid flowing in a random potential

The phase structures of driven quantum many-body systems have attracted considerable interest owing to recent experimental progress in ultracold atomic gases. A fundamental issue in this subject is to clarify how and when the long-range order of a nonequilibrium steady state is destroyed by random perturbations. In thermal equilibrium, the Mermin-Wagner theorem can be invoked to address the stability of the ordered phase against thermal fluctuations. However, in nonequilibrium situations the universal mechanisms responsible for the breakdown of the long-range order are poorly understood. In this study, we investigate the stability of the off-diagonal long-range order of a superfluid flowing in a weak random potential [1]. Within the classical field theory, we show that for an arbitrarily small flow velocity the off-diagonal long-range order is destroyed in one and two dimensions. We argue that the superfluid flowing in a random potential can be identified with the corresponding uniform system at thermal equilibrium with an effective temperature, where the long-range order is prohibited in one and two dimensions by the Mermin-Wagner theorem.

[1] Taiki Haga and Masahito Ueda, arXiv:1909.11997.