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 by using the stochastic projected Gross-Pitaevskii equation, 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. 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, while 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.