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

TL;DR

This paper derives equations describing the transition to Bose-Einstein condensation, focusing on interference effects and boundary layer formation during the process, based on quantum particle dynamics and blow-up phenomena.

Contribution

It introduces a new set of equations capturing the onset of interference effects during Bose-Einstein condensate formation, extending classical kinetic theory to quantum regimes.

Findings

Derived boundary layer equations for transition to BEC

Identified blow-up behavior in the Uehling-Uhlenbeck equation

Described quantum interference effects during condensate formation

Abstract

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.