The generalized Fokker — Planck kinetic equation of open quantum systems
DOI:
https://doi.org/10.15407/dopovidi2018.01.003Keywords:
correlations of states, Fokker — Planck kinetic equation, open quantum systemAbstract
The problem of the rigorous derivation of a generalized Fokker — Planck kinetic equation from the dynamics of open quantum systems in the presence of correlations of the initial states is considered. The process of the propagation of correlations in such many-particle quantum systems is described.
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Kapral, R. J. (2015). Phys.: Condens. Matter., 27, 073201.
Breuer, H.-P. & Petruccione, F. (2002). The Theory of Open Quantum System. Oxford Univ. Press.
Rivas, A. & Huelga, S. F. (2012). Open Quantum Systems. An Introduction. Berlin: Springer. doi: https://doi.org/10.1007/978-3-642-23354-8
Figari, R. & Teta, A. (2014). Quantum Dynamics of a Particle in a Tracking Chamber. Berlin, Heidelberg: Springer. doi: https://doi.org/10.1007/978-3-642-40916-5
Zagorodny, A. G. & Momot, A. I. (2015). Introduction to kinetic theory of plasma. Kiev: Naukova Dumka.
Deckert, D.-A., Frölich, J., Pickl, P. & Pizzo, A. (2014). Commun. Math. Phys., 328, No. 2, pp. 597-624. doi: https://doi.org/10.1007/s00220-014-1987-z
Lebowitz, J. L., Sinai, Ya. G. & Chernov, N. I. (2002). Russ. Math. Surv., 57, No. 6, pp. 1045-1125. doi: https://doi.org/10.1070/RM2002v057n06ABEH000572
Erdös, L. (2007). Classical and quantum Brownian motion. Ann. Henri Poincaré, 8, pp. 621-685.
Erdös, L. (2012). Lecture notes on quantum Brownian motion. Quantum Theory from Small to Large Scales. Lecture notes of Les Houches summer school. V.95. Oxford Univ. Press. doi: https://doi.org/10.1093/acprof:oso/9780199652495.003.0001
Bodineau, T., Gallagher, I. & Saint-Raymond, L. (2016). Invent. Math., 203, No. 2, pp. 493-553. doi: https://doi.org/10.1007/s00222-015-0593-9
Bogolyubov, N. N. (1978). Physics of Elementary Particles and Atomic Nuclei, 9, No. 4, pp. 501-579.
Gerasimenko, V. I. & Gapyak, I. V. (2012). Math. Bulletin Sh. Sci. Soc., 9, pp. 23-43.
Gerasimenko, V. I. & Gapyak, I. V. (2014). The non-Markovian Fokker—Planck kinetic equation for a system of hard spheres. Dopov. Nac. akad. nauk Ukr., No. 12, pp. 29-35 (in Ukrainian).
Gerasimenko, V. I. & Gapyak, I. V. (2015). The Fokker─Planck equation with initial correlations in collisional kinetic theory. Bukovina Math. J., 3, No. 3-4, pp. 52-58.
Gerasimenko, V. I. (2013). Statistical Mechanics and Random Walks: Principles, Processes and Applications. N.Y.: Nova Science Publ., Inc., pp. 233-288.
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