Equilibration of Quantum Gases

Terry Farrelly

Published 2015-12-08Version 1

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions for coarse measurements when inter-particle interactions are negligible. To do this, we show that solving the N particle equilibration problem is equivalent to solving a single-particle equilibration problem. We look at some examples, including N fermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate in time O(1/N). We also show that, for these coarse measurements, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, the timescale generally appears to be, at worst, polynomial in N.