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arXiv:1201.1269

The Kramers Problem for Quantum Fermi Gases with Velocity - Dependent Collision Frequency and Specular - Diffusive Boundary Conditions

A. Yu. Kvashnin, Latyshev, A. V., Aleksandr Alekseevich Yushkanov

Published Jan 5, 2012• 0 citations
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Abstract

The classical Kramers problem of the kinetic theory is solved. The Kramers problem about isothermal sliding for quantum Fermi gases is considered. Quantum gases with the velocity - dependent collision frequency are considered. Specular - diffusive boundary conditions are applied. Dependence of isothermal sliding on the resulted chemical potential is found out.

DOI
10.48550/arxiv.1201.1269

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The classical Kramers problem of the kinetic theory is solved. The Kramers problem about isothermal sliding for quantum Fermi gases is considered. Quantum gases with the velocity - dependent collision frequency are considered. Specular - diffusive boundary conditions are applied. Dependence of isothermal sliding on the resulted chemical potential is found out.
A solution is obtained for Kramers’ problem of isothermal slip of a quantum Bose gas along a flat solid surface. The reflection of molecules from the wall is assumed to be specular-diffuse. A model kinetic equation with a collision integral in the τ-model form and collision frequency proportional to the molecular velocity is used. The dependence of the slip velocity on the value of a parameter equal to the ratio of the chemical potential to the product of Boltzmann’s constant by the absolute temperature is analyzed.
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.
The interaction of a plane monochromatic traveling wave with two-level particles suffering collisions with buffer-gas particles is considered. Collision rates are assumed to be velocity dependent. The collision integral is obtained on the basis of the strong-collision model, generalized to the case of velocity-dependent collision rates (the so-called ``kangaroo'' model). We obtained the exact analytical solution of the problem for arbitrary intensity of radiation, arbitrary ratio of homogeneous and Doppler widths of the absorption line, and arbitrary mass ratio between absorbing- and buffer-gas particles. The obtained analytical solutions of the quantum kinetic equations allowed us to analyze the spectral shape of the strong-field absorption line as well as the probe-field absorption line (the nonlinear part of the work done by the probe field) and the frequency dependence of the light-induced drift (LID) velocity. A comprehensive comparative analysis for the three- and one-dimensional versions of the model is given. On the basis of this analysis, we reach the conclusion that the one-dimensional quantum kinetic equation has quite a wide range of application. We also reveal the conditions for the strongest manifestation of the velocity dependence of the collision rates, which affects most strongly the anomalous LID.