The generalized Fokker — Planck kinetic equation of open quantum systems

Authors

  • V.I. Gerasimenko Institute of Mathematics of the NAS of Ukraine, Kyiv

DOI:

https://doi.org/10.15407/dopovidi2018.01.003

Keywords:

correlations of states, Fokker — Planck kinetic equation, open quantum system

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.

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References

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.

Published

24.04.2024

How to Cite

Gerasimenko, V. (2024). The generalized Fokker — Planck kinetic equation of open quantum systems. Reports of the National Academy of Sciences of Ukraine, (1), 3–9. https://doi.org/10.15407/dopovidi2018.01.003