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We derive semiclassical transport equations for a trapped atomic Fermi gas inthe BCS phase at temperatures between zero and the superfluid transitiontemperature. These equations interpolate between the two well-known limitingcases of superfluid hydrodynamics at zero temperature and the Vlasov equationat the critical one. The linearized version of these equations, valid for smalldeviations from equilibrium, is worked out and applied to two simple exampleswhere analytical solutions can be found: a sound wave in a uniform medium andthe quadrupole excitation in a spherical harmonic trap. In spite of somesimplifying approximations, the main qualitative results of quantum mechanicalcalculations are reproduced, which are the different frequencies of thequadrupole mode at zero and the critical temperature and strong Landau dampingat intermediate temperatures. In addition we suggest a numerical method forsolving the semiclassical equations without further approximations.Comment: 15 pages, 4 figures; v2: discussion and references adde

Dynamics of a trapped Fermi gas in the BCS phase