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

As a test of the Kibble-Zurek mechanism (KZM) of defect formation, we simulate the Bose-Einstein condensation transition in a toroidally confined Bose gas using the stochastic projected Gross-Pitaevskii equation (SPGPE), with and without the energy-damping reservoir interaction. Energy-damping alters the scaling of the winding number distribution with the quench time - a departure from 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 reservoir interaction theory. The energy-damping reservoir interactions cause significant modification of the dynamical critical exponent of the phase transition, whilst preserving the essential KZM critical scaling behavior. Comparison of numerical and analytical two-point correlation functions further illustrates the effect of energy damping on the correlation length during freeze out.