Geodesic
Properties of translationally invariant quantum-dynamical semigroups
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 3, pp. 366-379 Cet article a éte moissonné depuis la source Math-Net.Ru

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A large class of translationally invariant quantum-dynamical semigroups on a $C^*$ algebra is considered. Conditions that ensure uniqueness of an invariant state and relaxation to it are found. The properties of the dynamical semigroups which arise in the rigorous derivation of the quantum kinetic equations for a Schrödinger particle in the translationaily invariant case are studied. 
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     author = {A. D. Manita},
     title = {Properties of translationally invariant quantum-dynamical semigroups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1991_89_3_a2/}
}
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A. D. Manita. Properties of translationally invariant quantum-dynamical semigroups. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 3, pp. 366-379. http://geodesic.mathdoc.fr/item/TMF_1991_89_3_a2/

[1] Davies E. B., Quantum theory of open systems, Academic Press, London, 1976 | MR

[2] Van Hove L., Physica, 21 (1955), 617–640 | MR

[3] Pule G. V., Commun. Math. Phys., 38 (1974), 241–256 | DOI | MR

[4] Davies E. B., Commun. Math. Phys., 39 (1974), 91–110 | DOI | MR | Zbl

[5] Gorini V., Frigerio A., Verri M., Kossakowski A., Sudarshan E. C. G., Rep. Math. Phys., 13 (1978), 149–173 | DOI | MR | Zbl

[6] Spohn H., Rev. Mod. Phys., 52 (1980), 569–615 | DOI | MR

[7] Domnenkov A. Sh., TMF, 79:2 (1989), 263–271 | MR

[8] Botvich D. D., Malyshev V. A., Commun. Math. Phys., 91 (1983), 301–312 | DOI | MR | Zbl

[9] Botvich D. D., Malyshev V. A., Izv. AN SSSR. Ser. matem., 54 (1990), 132–145 | MR | Zbl

[10] Domnenkov A. Sh., Malyshev V. A., DAN SSSR, 304 (1989), 326–329 | MR

[11] Malyshev V. A., Commun. Math. Phys., 119 (1988), 501–512 | DOI | MR

[12] Aizenshtadt V. V., Botvich D. D., Malyshev V. A., Itogi nauki i tekhniki. Teor. ver. Mat. stat. Teor. kiber., 27, VINITI, M., 1990, 3–78 | MR

[13] Lindblad G., Commun. Math. Phys., 48 (1976), 119–130 | DOI | MR | Zbl

[14] Spohn H., Rep. Math. Phys., 10 (1976), 189–194 | DOI | MR

[15] Spohn H., Lett. Math. Phys., 2 (1977), 33–38 | DOI | MR | Zbl

[16] Frigerio A., Lett. Math. Phys., 2 (1977), 79–87 | DOI | MR | Zbl

[17] Frigerio A., Commun. Math. Phys., 63 (1977), 269–276 | DOI | MR

[18] Frigerio A., Verri M., Math. Z., 180 (1982), 275 | DOI | MR | Zbl

[19] Bratteli U., Robinson D., Operatornye algebry i kvantovaya statisticheskaya mekhanika, Mir, M., 1982 | MR | Zbl

[20] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[21] Christensen E., Evans D. E., J. London Math. Soc. (2), 20 (1979), 358–368 | DOI | MR | Zbl

[22] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 1. Funktsionalnyi analiz, Mir, M., 1977 | MR

[23] Evans D. E., Hanche-Olsen, J. Func. Anal., 32 (1979), 207–212 | DOI | MR | Zbl

[24] Bratteli O., Robinson D., Operator algebras and quantum statistical mechanics, V. II, Springer, 1981 | MR | Zbl

[25] Manita A. D., Funktsionalnyi i stokhasticheskii analiz i ikh prilozheniya, eds. P. L. Ulyanov, B. V. Gnedenko, MGU, M., 1991, 54–58

[26] Botvich D. D., Malyshev V. A., Manita A. D., Helv. Phys. Acta, 64 (1991), 1072–1092 | MR

[27] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 2. Garmonicheskii analiz. Samosopryazhennost, Mir, M., 1978 | MR