Geodesic
Excessive maps, “arrival times” and perturbation of dynamical semigroups
Izvestiya. Mathematics, Tome 59 (1995) no. 6, pp. 1311-1325 Cet article a éte moissonné depuis la source Math-Net.Ru

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The notion of excessive map for dynamical semigroup is introduced, and it is shown that an excessive map defines an operation-valued measure describing the measurement of an “arrival time” related to the irreversible dynamics described by the semigroup. Any such arrival time determines a positive perturbation of the dynamical semigroup describing the dynamics after “arrivals”. Generators of the relevant perturbations are characterized, and several examples, both commutative and a non-commutative, are discussed, elucidating the problem of standard representation. 
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A. S. Holevo. Excessive maps, “arrival times” and perturbation of dynamical semigroups. Izvestiya. Mathematics, Tome 59 (1995) no. 6, pp. 1311-1325. http://geodesic.mathdoc.fr/item/IM2_1995_59_6_a9/

[1] Bhat B. V., Parthasarathy K. R., “Markov dilations of non-commutative dynamical semigroups and a quantum boundary theory”, Ann. Inst. H. Poincare. Ser. B, 1994

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

[3] Chebotarev A. M., “Neobkhodimye i dostatochnye usloviya konservativnosti dinamicheskikh polugrupp”, Itogi nauki i tekhniki. Sovr. probl. matematiki. Noveishie dostizheniya, 36, VINITI, M., 1989, 149–184 | MR | Zbl

[4] Davies E. B., Quantum Theory of Open Systems, AP, London, 1976 | MR

[5] Davies E. B., “Quantum dynamical semigroups and the neutron diffusion equation”, Rept. Math. Phys., 11 (1977), 169–188 | DOI | MR | Zbl

[6] Fagnola F., Characterization of isometries and unitary weakly differentiable cocycles in Fock space, Preprint UTM 358, University of Trento, 1991 | MR

[7] Kholevo A. S., Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, Nauka, M., 1980 | MR | Zbl

[8] Kholevo A. S., “Struktura kovariantnykh dinamicheskikh polugrupp”, Dokl. RAN, 328 (1993), 666–670 | MR | Zbl

[9] Ludwig G., Foundations of Quantum Mechanics, Springer-Verlag, Berlin, 1983 | MR