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We develop a microscopic theory of sound damping due to Landau mechanism indilute gas with Bose condensate. It is based on the coupled evolution equationsof the parameters describing the system. These equations have been derived inearlier works within a microscopic approach which employs thePeletminskii-Yatsenko reduced description method for quantum many-particlesystems and Bogoliubov model for a weakly nonideal Bose gas with a separatedcondensate. The dispersion equations for sound oscillations were obtained bylinearization of the mentioned evolution equations in the collisionlessapproximation. They were analyzed both analytically and numerically. Theexpressions for sound speed and decrement rate were obtained in high and lowtemperature limiting cases. We have shown that at low temperature thedependence of the obtained quantities on temperature significantly differs fromthose obtained by other authors in the semi-phenomenological approaches.Possible effects connected with non-analytic temperature dependence ofdispersion characteristics of the system were also indicated.

Mechanism of collisionless sound damping in dilute Bose gas with condensate