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We study the sympathetic cooling of a trapped Fermi gas interacting with anideal Bose gas below the critical temperature of the Bose-Einsteincondensation. We derive the quantum master equation, which describes thedynamics of the fermionic component, and postulating the thermal distributionfor both gases we calculate analytically the rate at which fermions are cooledby the bosonic atoms. The particle losses constitute an important source ofheating of the degenerate Fermi gas. We evaluate the rate of loss-inducedheating and derive analytical results for the final temperature of fermions,which is limited in the presence of particle losses.Comment: 7 pages, 2 figures, EPL style; final versio

Sympathetic cooling of trapped fermions by bosons in the presence of particle losses