  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 quasi-exact
numerical simulations, we show that the two phases are separated by a
Kosterlitz-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 non-equilibrium quantum gases and nonlinear, classical wave systems.
