We study the dynamical evolution of a two-dimensional Bose gas after a disorder potential quench. Depending on the initial conditions, the system evolves either to a thermal or a superfluid state. Using extensive quasiexact numerical simulations, we show that the two phases are separated by a Kosterliz-Thouless transition. The thermalization time is shown to be longer in the superfluid phase, but no critical slowing down is observed at the transition. The long-time phase diagram is well reproduced by a simple theoretical model. The spontaneous emergence of Kosterlitz-Thouless transitions following a quench is a generic phenomenon that should arise both in the context of nonequilibrium quantum gases and in the context of nonlinear classical wave systems.

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• BKT transition
• Cold atoms & matter waves
• Nonequilibrium systems
• Random & disordered media
• Superfluids