Abstract:
The collision integrals in the Fokker–Planck and Boltzmann equations are renormalized. The renormalized collision integrals take into account the influence of the “medium” on two-particle collisions, this giving rise to a natural cutoff of the correlation functions at times and lengths of the order of the mean free time and the mean free path, respectively, of the molecules.
Citation:
D. N. Zubarev, M. Yu. Novikov, “Renormalized kinetic equations for a system with weak interaction and for a low-density gas”, TMF, 19:2 (1974), 237–251; Theoret. and Math. Phys., 19:2 (1974), 480–490
\Bibitem{ZubNov74}
\by D.~N.~Zubarev, M.~Yu.~Novikov
\paper Renormalized kinetic equations for a~system with weak interaction and for a~low-density gas
\jour TMF
\yr 1974
\vol 19
\issue 2
\pages 237--251
\mathnet{http://mi.mathnet.ru/tmf3582}
\transl
\jour Theoret. and Math. Phys.
\yr 1974
\vol 19
\issue 2
\pages 480--490
\crossref{https://doi.org/10.1007/BF01035949}
Linking options:
https://www.mathnet.ru/eng/tmf3582
https://www.mathnet.ru/eng/tmf/v19/i2/p237
This publication is cited in the following 9 articles:
M. V. Tokarchuk, “To the kinetic theory of dense gases and liquids. Calculation of quasi-equilibrium particle distribution functions by the method of collective variables”, Math. Model. Comput., 9:2 (2022), 440
F. S. Vannucchi, Á. R. Vasconcellos, R. Luzzi, “Dynamics of a Bose-Einstein condensate of excited magnons”, Eur. Phys. J. B, 86:11 (2013)
Mitsusada M. Sano, “Zero-Collision Term Problem in Kinetic Theory of One-Dimensional Systems”, J. Phys. Soc. Jpn., 81:2 (2012), 024008
Yu. N. Barabanenkov, V. D. Ozrin, A. V. Shelest, “Theory of stochastic processes in quantum dynamical systems”, Theoret. and Math. Phys., 42:2 (1980), 152–159
D. N. Zubarev, “Contemporary methods of the statistical theory of nonequilibrium processes”, J. Soviet Math., 16:6 (1981), 1509–1571
V. P. Kalashnikov, M. I. Auslender, “Generating Functionals in Nonequilibrium Statistical Mechanics”, Fortschr. Phys., 27:8 (1979), 355
S. I. Kantorovich, “Construction of renormalized collision integral for a quantum gas”, Soviet Physics Journal, 21:8 (1978), 1066
B. M. Gurevich, V. I. Oseledets, “Some mathematical problems related to the nonequilibrium statistical mechanics of infinitely many particles”, J. Soviet Math., 13:4 (1980), 455–478
R. M. Yul'met'yev, “Bogolyubov's abridged description of equilibrium systems and derivation of an equation for the radial distribution function in a liquid”, Theoret. and Math. Phys., 25:2 (1975), 1100–1108
Citation in format AMSBIB
Contact us: