Title | The generalized Fokker — Planck kinetic equation of open quantum systems |
Publication Type | Journal Article |
Year of Publication | 2018 |
Authors | Gerasimenko, VI |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2018.01.003 |
Issue | 1 |
Section | Mathematics |
Pagination | 3-9 |
Date Published | 1/2018 |
Language | Ukrainian |
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. |
Keywords | correlations of states, Fokker — Planck kinetic equation, open quantum system |
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.