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We use the mean-field approximation to simplify the master equation forsympathetic cooling of Bosons. For the mean single-particle occupation numbers,this approach yields the same equations as the factorization assumptionintroduced in an erlier paper. The stationary or equilibrium solution of theresulting master equation for the one-body density matrix shows that themean-field approximation breaks down whenever the fraction of condensate Bosonsexceeds ten percent or so of the total. Using group-theoretical methods, wealso solve the time-dependent master equation for the one-body density matrix.Given the time dependence of the mean single-particle occupation numbers, thissolution is obtained by quadratures. It tends asymptotically towards theequilibrium solution.Comment: submitted to PR

Mean-field approximation to the master equation for sympathetic cooling of trapped bosons