On the onset of interference effects during the formation of the Bose-Einstein condensate

Details On the onset of interference effects during the formation of the Bose-Einstein condensate On the onset of interference effects during the formation of the Bose-Einstein condensate

2008-03-27

arxiv.org/abs/0803.3870v1

Physics

Mathematical Physics

Scientific paper

In this paper we derive the equations characterizing the boundary layer which describes the transition of the distribution function of a gas of weakly interacting bosons to the distribution function of the gas in the presence of a Bose-Einstein condensate. To this end, we first rederive the classical Uehling-Uhlenbeck equation taking as a starting point the dynamics of a system of many weakly interacting quantum particles. The solutions of the Uehling-Uhlenbeck equation yield blow-up in finite time. Near the blow-up time the approximations used to derive the Uehling-Uhlenbeck equation break down. We derive the set of equations that describe the building of correlations and the onset of quantum interference effects for the many-particle hamiltonian system under the assumption that the blow-up for the Uehling-Uhlenbeck equation takes place in a self-similar form.

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