Yurii Slyusarenko, Oleksandr Kriuchkov
We develop a microscopic theory of sound damping due to Landau mechanism in dilute gases with a Bose condensate. It is based on the coupled equations that take into account the mutual influence of condensate density, phase (or superfluid velocity), and distribution function of elementary excitations on evolution of the system. These equations have been derived in earlier works within a microscopic approach which employs the Peletminskii-Yatsenko reduced description method for quantum many-particle systems and Bogoliubov model for a weakly nonideal Bose gas with a separated condensate. The dispersion equations for sound oscillations are obtained by linearization of the mentioned evolution equations in the collisionless approximation. They are analyzed both analytically and numerically. The expressions for speed of sound and decrement factor of sound are obtained in the limiting cases of high and low temperatures. It is shown that at low temperatures, the decrement of collisionless damping of sound has a quadratic dependence on temperature. Such dependence essentially differs from that obtained earlier by other authors in phenomenological approaches. It is also demonstrated that at high temperatures, the sound damping coefficient has a linear dependence on temperature that coincides with earlier results of other authors. We discover a finite temperature at which the speed of sound is exactly equal to the speed of sound at zero temperature. This effect is due to non-analytic dependence of dispersion characteristics of the system on temperature at this point. We also indicate the possibility of oscillations for the decrement or increment coefficients of sound in the vicinity of the discovered temperature.
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http://arxiv.org/abs/1208.1653
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