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arXiv:1001.0407

Smoluchowski problem for degenerate Bose gases

Latyshev, A. V., Aleksandr Alekseevich Yushkanov

Published Jan 3, 2010• 3 citations
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Abstract

We construct a kinetic equation simulating the behavior of degenerate quantum Bose gases with the collision rate proportional to the molecule velocity. We obtain an analytic solution of the half--space boundary--value Smoluchowski problem of the temperature jump at the interface between the degenerate Bose gas and the condensed phase.
DOI
10.48550/arxiv.1001.0407

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The relaxation kinetics of an ideal Bose gas coupled to a phonon bath at temperatures below or equal to the critical temperature Tc{\mathrm{T}}_{\mathrm{c}}Tc​ is given within a unique scenario. During the first transient stage, which lasts a few characteristic scattering times, the initial distribution disappears. The following nonexponential relaxation towards a quantum degenerate equilibrium state with a Bose-Einstein condensate is a slow adiabatic process. For this second kinetic stage we find an analytic generic solution of the Boltzmann equation. The generic solution is independent of the initial distribution and completely defined by the ratio Tc{\mathrm{T}}_{\mathrm{c}}Tc​/Tb{\mathrm{T}}_{\mathrm{b}}Tb​ of the critical and bath temperatures.
Distribution of mass velocity of quantum Bose-gas in half-space is received. Far from half-space border the gradient of mass velocity is set. The mass velocity of Bose-gas directly at a wall is found also. All results are received on basis of the analytical solution of Kramer's problem. The analysis of dependence of velocity coefficients from parametre quantity is carried out. The parametre representing the relation of chemical potential to product of Boltzmann constant on absolute temperature. Graphic comparison of coefficients of velocity Bose- and Fermi-gases is resulted.
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