Quantum Non-Markovian Stochastic Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 1, pp. 87-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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We derive quantum diffusion equations with transport coefficients explicitly depending on time from generalized non-Markovian Langevin equations and obtain generalized fluctuation-dissipation relations. We substantiate the axiomatic Lindblad approach in the microscopic model. For non-Markovian dynamics, we find sets of diffusion coefficients that ensure the purity of states at any instant.
Keywords: open quantum systems, non-Markovian dynamics.
Mots-clés : friction and diffusion coefficients
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G. G. Adamian; N. V. Antonenko; Z. Kanokov; V. V. Sargsyan. Quantum Non-Markovian Stochastic Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 1, pp. 87-101. http://geodesic.mathdoc.fr/item/TMF_2005_145_1_a3/

[1] N. N. Bogolyubov, Izbrannye trudy v trekh tomakh, Naukova Dumka, Kiev, 1971 ; А. А. Белавин, Б. Я. Зельдович, А. М. Переломов, Б. С. Попов, ЖЭТФ, 56 (1969), 264; A. O. Caldeira, A. J. Leggett, Physica A, 121 (1983), 587 ; Ann. Phys., 149 (1983), 374 ; H. J. Carmichael, An Open System Approach to Quantum Optics, Springer, Berlin, 1993 ; Ю. Л. Климонтович, Статистическая теория открытых систем, Т. 1, 1995; Т. 2, 1999; Т. 3, Янус, М., 2001; V. V. Dodonov, O. V. Man'ko, V. I. Man'ko, J. of Russian Laser Research, 16 (1995), 1 | MR | DOI | MR | Zbl | DOI | DOI

[2] N. G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981 | MR

[3] C. W. Gardiner, Quantum Noise, Springer, Berlin, 1991 | MR | Zbl

[4] D. Zubarev, V. Morozov, G. Röpke, Statistical Mechanics of Nonequilibrium Processes. V. 2. Relaxation and Hydrodynamic Processes, Akademie Verlag, Berlin, 1997 | MR | Zbl

[5] U. Weiss, Quantum Dissipative Systems, World Scientific, Singapore, 1999 | MR

[6] K. Lindenberg, B. West, Phys. Rev. A, 30 (1984), 568 | DOI | MR

[7] F. Haake, R. Reibold, Phys. Rev. A, 32 (1985), 2462 ; P. Talkner, Ann. Phys., 167 (1986), 390 ; B. L. Hu, J. P. Paz, Y. Zhang, Phys. Rev. D, 45 (1992), 2843 ; R. Karrlein, H. Grabert, Phys. Rev. E, 55 (1997), 153 | DOI | DOI | MR | DOI | MR | Zbl | DOI

[8] H. Grabert, P. Schramm, G.-L. Ingold, Phys. Rep., 168 (1988), 115 | DOI | MR

[9] G. Lindblad, Commun. Math. Phys., 48 (1976), 119 ; Rep. Math. Phys., 10 (1976), 393 ; G. G. Adamian, N. V. Antonenko, W. Scheid, Phys. Lett. A, 244 (1998), 482 ; 260 (1999), 39 ; Yu. V. Palchikov, G. G. Adamian, N. V. Antonenko, W. Scheid, J. Phys. A, 33 (2000), 4265 ; Physica A, 316 (2002), 297 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[10] H. Dekker, Phys. Rep., 80 (1981), 1 | DOI | MR

[11] V. V. Dodonov, V. I. Manko, Tr. FIAN, 167, 1986, 7 ; 183, 1987, 5 ; V. V. Dodonov, E. V. Kurmyshev, V. I. Man'ko, Phys. Lett. A, 79 (1980), 150 | MR | MR | DOI | MR

[12] A. Isar, A. Sandulescu, H. Scutaru, E. Stefanescu, W. Scheid, Int. J. Mod. Phys. E, 3 (1994), 635 ; A. Isar, Fortschr. Phys., 47 (1999), 855 | DOI | MR | 3.0.CO;2-Z class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[13] V. G. Zelevinskii, “Problemy v teorii reaktsii s tyazhelymi ionami”, Materialy XII Zimnei shkoly LIYaF, Izd-vo LIYaF, L., 1978, 53; Р. В. Джолос, С. П. Иванова, В. В. Иванов, ЯФ, 40 (1984), 117; S. P. Ivanova, R. V. Jolos, Nucl. Phys. A, 530 (1991), 232 | DOI