Kinetics of Bose-Einstein Condensation in a Trap

The formation process of a Bose-Einstein condensate in a trap is described using a master equation based on quantum kinetic theory, which can be well approximated by a description using only the condensate mode in interaction with a thermalized bath of noncondensate atoms. A rate equation of the form $\dot{n}{=2W}^{+}\left(n\right)[\left({1-e}^{\{{\mu }_n-\mu \}/\mathrm{kT}}\right)n+1\mathrm{}]$ is derived, in which the difference between the condensate chemical potential ${\mu }_n$ and the bath chemical potential $\mu$ gives the essential behavior. Solutions of this equation give a characteristic latency period for condensate formation and appear to be consistent with the observed behavior of both rubidium and sodium condensate formation.