Geodesic
Kinetic Equation for Quantum Fermi Gases and the Analytic Solution of Boundary Value Problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 2, pp. 310-324

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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, chemical potential jumps.
Mots-clés : concentration jumps 
@article{TMF_2003_134_2_a10,
     author = {A. V. Latyshev and A. A. Yushkanov},
     title = {Kinetic {Equation} for {Quantum} {Fermi} {Gases} and the {Analytic} {Solution} of {Boundary} {Value} {Problems}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {310--324},
     publisher = {mathdoc},
     volume = {134},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a10/}
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A. V. Latyshev; A. A. Yushkanov. Kinetic Equation for Quantum Fermi Gases and the Analytic Solution of Boundary Value Problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 2, pp. 310-324. http://geodesic.mathdoc.fr/item/TMF_2003_134_2_a10/