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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 2003 Volume 134, Number 2, Pages 310–324 (Mi tmf152)

This article is cited in 7 papers

Kinetic Equation for Quantum Fermi Gases and the Analytic Solution of Boundary Value Problems

A. V. Latyshev, A. A. Yushkanov

Moscow Pedagogical University, Moscow, Russian Federation

Abstract: We construct a kinetic equation describing the behavior of quantum Fermi gases with the molecule collision frequency proportional to the molecule velocity. We obtain an analytic solution of the generalized Smoluchowski problem with the temperature gradient and the mass flow velocity specified away from the surface. We find exact formulas for jumps of the gas temperature, concentration, and chemical potential. Analysis of limit cases demonstrates a transition of the quantum Fermi gas to the classical or degenerate gas.

Keywords: boundary value problem, kinetic equation, dilute Fermi gas, distribution function, generalized Smoluchowski problem, temperature jumps, concentration jumps, chemical potential jumps.

Received: 14.12.2001
Revised: 22.04.2002

DOI: 10.4213/tmf152


 English version:
Theoretical and Mathematical Physics, 2003, 134:2, 271–284

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