Half-Space Problems for a Linearized Discrete Quantum Kinetic Equation
2015 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 159, no 2, 358-379 p.Article in journal (Refereed) Published
We study typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer, for a general discrete model of a quantum kinetic equation for excitations in a Bose gas. In the discrete case the plane stationary quantum kinetic equation reduces to a system of ordinary differential equations. These systems are studied close to equilibrium and are proved to have the same structure as corresponding systems for the discrete Boltzmann equation. Then a classification of well-posed half-space problems for the homogeneous, as well as the inhomogeneous, linearized discrete kinetic equation can be made. The number of additional conditions that need to be imposed for well-posedness is given by some characteristic numbers. These characteristic numbers are calculated for discrete models axially symmetric with respect to the x-axis. When the characteristic numbers change is found in the discrete as well as the continuous case. As an illustration explicit solutions are found for a small-sized model.
Place, publisher, year, edition, pages
Springer, 2015. Vol. 159, no 2, 358-379 p.
Bose-Einstein condensate, Low temperature kinetics, Discrete kinetic equation, Milne problem, Kramer problem
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kau:diva-35795DOI: 10.1007/s10955-015-1190-4ISI: 000351690500010OAI: oai:DiVA.org:kau-35795DiVA: diva2:802137