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 ${ ̇ \.{}{}}{n}{{{0ex}{0ex}}={{0ex}{0ex}}2W}⁺(n)[({1{-}e}^{{{{μ}}ₙ{-}{μ}}/kT})n+1]$ is derived, in which the difference between the condensate chemical potential ${{μ}}ₙ$ and the bath chemical potential ${μ}$ 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.