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Quantum detailed balance and KMS condition

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Abstract

A definition of detailed balance for quantum dynamical semigroups is given, and its close connection with the KMS condition is investigated.

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References

  1. Agarwal, G.S.: Z. Physik258, 409–422 (1973)

    Google Scholar 

  2. Carmichael, H.J., Walls, D.F.: Z. Physik B23, 299–306 (1976)

    Google Scholar 

  3. Alicki, R.: Rep. Math. Phys.10, 249–258 (1976)

    Google Scholar 

  4. Gorini, V., Frigerio, A., Verri, M., Kossakowski, A., Sudarshan, E.C.G.: Properties of quantum markovian master equations. Rep. Math. Phys. (to appear)

  5. Ingarden, R.S., Kossakowski, A.: Ann. Phys. (N.Y.)89, 451–485 (1975)

    Google Scholar 

  6. Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: J. Math. Phys.17, 821–825 (1976)

    Google Scholar 

  7. Lindblad, G.: Commun. math. Phys.48, 119–130 (1976)

    Google Scholar 

  8. Kossakowski, A.: Bull. Acad. Polon. Sci. Math. (to appear)

  9. Evans, D.E., Lewis, J.T.: Completely positive maps on the CCR algebras. J. Funct. Anal. (to appear)

  10. Takesaki, M.: Tomita's theory of modular Hilbert algebras and its applications. Lecture notes in mathematics, Vol. 128. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  11. Sirugue, M., Winnink, M.: Commun. math. Phys.19, 161–168 (1970)

    Google Scholar 

  12. Bratteli, O., Robinson, D.W.: Ann. Inst. H. Poincaré25, 139–164 (1976)

    Google Scholar 

  13. Sakai, S.:C*-algebras andW*-algebras. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  14. Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. II. New York: Academic Press 1975

    Google Scholar 

  15. Davies, E.B.: Commun. math. Phys.49, 113–129 (1976)

    Google Scholar 

  16. Arveson, W.B.: Acta Math.123, 141–224 (1969)

    Google Scholar 

  17. Kraus, K.: Ann. Phys. (N.Y.)64, 311–335 (1971)

    Google Scholar 

  18. Gorini, V., Kossakowski, A.: J. Math. Phys.17, 1298–1305 (1976)

    Google Scholar 

  19. Frigerio, A., Gorini, V.: J. Math. Phys.17, 2123–2127 (1976)

    Google Scholar 

  20. Davies, E.B.: Commun. math. Phys.39, 91–110 (1974)

    Google Scholar 

  21. Haag, R., Kastler, D., Trych-Pohlmeyer, E.: Commun. math. Phys.38, 173–193 (1974)

    Google Scholar 

  22. Emch, G.G.: Algebraic methods in statistical mechanics and quantum field theory. New York: Wiley-Interscience 1972

    Google Scholar 

  23. Sewell, G.L.: Ann. Phys. (N.Y.)85, 336–377 (1974)

    Google Scholar 

  24. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  25. Radin, C.: Commun. math. Phys.21, 291–302 (1971)

    Google Scholar 

  26. Evans, D.E.: Commun. math. Phys.54, 293–297 (1977)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Physics, N. Copernicus University, Toruń, Poland

    Andrzej Kossakowski

  2. Istituto di Fisica dell' Università, Milano

    Alberto Frigerio & Vittorio Gorini

  3. Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Milano, Italy

    Alberto Frigerio, Vittorio Gorini & Maurizio Verri

  4. Istituto di Matematica del Politecnico, Milano

    Maurizio Verri

Authors
  1. Andrzej Kossakowski
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  2. Alberto Frigerio
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  3. Vittorio Gorini
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  4. Maurizio Verri
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Additional information

Communicated by H. Araki

A fellowship from the Italian Ministry of Public Education is acknowledged

A fellowship from the Italian National Research Council is acknowledged

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Kossakowski, A., Frigerio, A., Gorini, V. et al. Quantum detailed balance and KMS condition. Commun.Math. Phys. 57, 97–110 (1977). https://doi.org/10.1007/BF01625769

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  • DOI: https://doi.org/10.1007/BF01625769

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