Theory of transverse acoustic impedance of superfluid 3He

A microscopic theory of transverse acoustic impedance of superfluid He-3 is presented. We calculate the stress tensor of superfluid He-3 as a response to the oscillating rough wall. For that purpose, we extend a quasi-classical theory with the random S-matrix model for the rough wall to time dependent problems. By this formulation, we can take into account the pair breaking mechanism. Our numerical results show good agreement with the recent experiments in both the A-phase and the B-phase. We discuss that the frequency and the temperature dependence of the transverse acoustic impedance is dominated by the pair excitations involving the surface bound states.