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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 2, Pages 205–221 (Mi izv19)  

This article is cited in 17 scientific papers (total in 17 papers)

On translation-covariant quantum Markov equations

A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The structure of quantum Markov control equations with unbounded generators and covariant with respect to 1) irreducible representation of the Weyl CCR on $R^d$ and 2) representation of the group of $R^d$, is completely described via non-commutative Levy–Khinchin-type formulae. The existence and uniqueness of solutions for such equations is briefly discussed.

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English version:
Izvestiya: Mathematics, 1995, 59:2, 427–443

Bibliographic databases:

MSC: 34F05
Received: 21.03.1994

Citation: A. S. Holevo, “On translation-covariant quantum Markov equations”, Izv. RAN. Ser. Mat., 59:2 (1995), 205–221; Izv. Math., 59:2 (1995), 427–443

Citation in format AMSBIB
\by A.~S.~Holevo
\paper On translation-covariant quantum Markov equations
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 2
\pages 205--221
\jour Izv. Math.
\yr 1995
\vol 59
\issue 2
\pages 427--443

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    This publication is cited in the following articles:
    1. Holevo A., “Covariant Quantum Markovian Evolutions”, J. Math. Phys., 37:4 (1996), 1812–1832  crossref  mathscinet  zmath  adsnasa  isi
    2. Holevo A., “Radon-Nikodym Derivatives of Quantum Instruments”, J. Math. Phys., 39:3 (1998), 1373–1387  crossref  mathscinet  zmath  adsnasa  isi
    3. Vacchini B., “Translation-Covariant Markovian Master Equation for a Test Particle in a Quantum Fluid”, J. Math. Phys., 42:9 (2001), 4291–4312  crossref  mathscinet  zmath  adsnasa  isi
    4. Vacchini B., “Quantum Optical Versus Quantum Brownian Motion Master Equation in Terms of Covariance and Equilibrium Properties”, J. Math. Phys., 43:11 (2002), 5446–5458  crossref  mathscinet  zmath  adsnasa  isi
    5. Vacchini B., “Dissipative Systems and Objective Description: Quantum Brownian Motion as an Example”, Int. J. Theor. Phys., 43:6 (2004), 1515–1525  crossref  mathscinet  zmath  isi
    6. Angelo Bassi, Emiliano Ippoliti, Bassano Vacchini, “On the energy increase in space-collapse models”, J Phys A Math Gen, 38:37 (2005), 8017  crossref  mathscinet  zmath  isi
    7. Francesco Petruccione, Bassano Vacchini, “Quantum description of Einstein’s Brownian motion”, Phys Rev E, 71:4 (2005), 046134  crossref  isi
    8. Bassano Vacchini, “Theory of Decoherence due to Scattering Events and Lévy Processes”, Phys Rev Letters, 95:23 (2005), 230402  crossref  isi
    9. Vacchini B., “Master-Equations for the Study of Decoherence”, Int. J. Theor. Phys., 44:7 (2005), 1011–1021  crossref  mathscinet  zmath  isi
    10. Bassi A., Ippoliti E., Vacchini B., “Dynamical Reduction Models and the Energy Conservation Principle”, Quantum Mechanics, AIP Conference Proceedings, 844, eds. Bassi A., Durr D., Weber T., Zanghi N., Amer Inst Physics, 2006, 8–21  mathscinet  zmath  isi
    11. Bassano Vacchini, “Non-Markovian dynamics for bipartite systems”, Phys Rev A, 78:2 (2008), 022112  crossref  mathscinet  isi
    12. Vacchini B., “Description of Decoherence by Means of Translation-Covariant Master Equations and Levy Processes”, Quantum Probability and Related Topics, Qp-Pq Quantum Probability and White Noise Analysis, 23, eds. Garcia J., Quezada R., Sontz S., World Scientific Publ Co Pte Ltd, 2008, 254–265  crossref  mathscinet  zmath  isi
    13. Bassano Vacchini, Klaus Hornberger, “Quantum linear Boltzmann equation”, Physics Reports, 478:4-6 (2009), 71  crossref  elib
    14. Marc Busse, Piotr Pietrulewicz, Heinz-Peter Breuer, Klaus Hornberger, “Stochastic simulation algorithm for the quantum linear Boltzmann equation”, Phys Rev E, 82:2 (2010), 026706  crossref
    15. Vacchini B., “Covariant Mappings for the Description of Measurement, Dissipation and Decoherence in Quantum Mechanics”, Theoretical Foundations of Quantum Information Processing and Communication, Lecture Notes in Physics, 787, eds. Bruning E., Petruccione F., Springer-Verlag Berlin, 2010, 39–77  crossref  mathscinet  zmath  adsnasa  isi
    16. Benoı̂t Descamps, “Asymptotically decreasing Lieb-Robinson velocity for a class of dissipative quantum dynamics”, J. Math. Phys, 54:9 (2013), 092202  crossref
    17. Gneiting C., Anger F.R., Buchleitner A., “Incoherent ensemble dynamics in disordered systems”, Phys. Rev. A, 93:3 (2016), 032139  crossref  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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