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Abstract

The generalized Langevin equation, which is derived by H. Mori,as a general, microscopic formulation of the stochastic theory of Brownian motions, is applied to evaluate the longitudinal attenuation rate of sound in weak-coupling, pure superconductors. In order to qualify the ultrasonic absorption as stochastic processes, the relaxation time of the random interactions on the phonon must be much shorter than the relaxation time of the phonon. We show that this is indeed the case by showing that the former is of the order of the relaxation time of the distribution function of the excitations from the BGS condensate. As compared, with the earlier result derived by first order perturbation theory, the inclusion of the life-time effect has improved the agreement with experimental data. When Ƭ≿Δ,ω, it is shown that Cooper pairs participate in the absorption processes even when ω