The generalized Fokker — Planck kinetic equation of open quantum systems

TitleThe generalized Fokker — Planck kinetic equation of open quantum systems
Publication TypeJournal Article
Year of Publication2018
AuthorsGerasimenko, VI
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2018.01.003
Issue1
SectionMathematics
Pagination3-9
Date Published1/2018
LanguageUkrainian
Abstract

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.

Keywordscorrelations of states, Fokker — Planck kinetic equation, open quantum system
References: 
  1. Kapral, R. J. (2015). Phys.: Condens. Matter., 27, 073201.
  2. Breuer, H.-P. & Petruccione, F. (2002). The Theory of Open Quantum System. Oxford Univ. Press.
  3. Rivas, A. & Huelga, S. F. (2012). Open Quantum Systems. An Introduction. Berlin: Springer. doi: https://doi.org/10.1007/978-3-642-23354-8
  4. 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
  5. Zagorodny, A. G. & Momot, A. I. (2015). Introduction to kinetic theory of plasma. Kiev: Naukova Dumka.
  6. 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
  7. 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
  8. Erdös, L. (2007). Classical and quantum Brownian motion. Ann. Henri Poincaré, 8, pp. 621-685.
  9. 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
  10. 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
  11. Bogolyubov, N. N. (1978). Physics of Elementary Particles and Atomic Nuclei, 9, No. 4, pp. 501-579.
  12. Gerasimenko, V. I. & Gapyak, I. V. (2012). Math. Bulletin Sh. Sci. Soc., 9, pp. 23-43.
  13. 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).
  14. 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.
  15. Gerasimenko, V. I. (2013). Statistical Mechanics and Random Walks: Principles, Processes and Applications. N.Y.: Nova Science Publ., Inc., pp. 233-288.