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As a test of the Kibble-Zurek mechanism (KZM) of defect formation, wesimulate the Bose-Einstein condensation transition in a toroidally confinedBose gas using the stochastic projected Gross-Pitaevskii equation (SPGPE), withand without the energy-damping reservoir interaction. Energy-damping alters thescaling of the winding number distribution with the quench time - a departurefrom the universal KZM theory that relies on equilibrium critical exponents.Numerical values are obtained for the correlation-length critical exponent$\nu$ and the dynamical critical exponent $z$ for each variant of reservoirinteraction theory. The energy-damping reservoir interactions cause significantmodification of the dynamical critical exponent of the phase transition, whilstpreserving the essential KZM critical scaling behavior. Comparison of numericaland analytical two-point correlation functions further illustrates the effectof energy damping on the correlation length during freeze out.

Reservoir interactions during Bose-Einstein condensation: modified critical scaling in the Kibble-Zurek mechanism of defect formation