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Dissipativity and the spectral property of the collision operator

✍ Scribed by Th.C. Guo; W.W. Guo

Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
181 KB
Volume
79
Category
Article
ISSN
0378-4371

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✦ Synopsis

It has been shown by the Brussels School that there is a physical representation in which the evolution of the density matrix reveals the dissipative structure. In this article, we present a two-dimensional model of the collision operator with a singularity at the origin which characterizes a long-range force. The dissipativity and the approach to equilibrium in the physical representation are studied and it is shown that the second law may be established in spite of the failure of Boltzmann's kinetic equation.

* The collision operator generally has a cut along the real axis. In this paper, we denote by ~p(z) the analytic continuation of the collision operator from above the real axis.

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