A rapid change of environment can force a system to cross the critical point of a phase transition at a finite rate. The transition causes defects to be spontaneously generated - remnants of the broken symmetry frozen into the new phase. The rate of crossing the transition determines density of defects formed: a faster quench creates smaller domains of spontaneously broken symmetry, resulting in a higher density of defects. This process is known as the Kibble-Zurek mechanism after Tom Kibble who came up with the idea, and Wojciech Zurek who made it into a quantitative tool able to explain experimental data.
A quantitative reservoir theory should allow for first-principles description of high-temperature BEC experiments, including spontaneous defect formation during the phase transition. We have developed and applied the Stochastic Projected GPE to modeling quenched Bose gases.
Papers on KZM are shown below.