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Quantum Langevin equation in the weak coupling limit

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References

  1. Accardi, L.: Quantum Markov chains. In: Proceedings of the School of Mathematical Physics, University of Camerino (1974).

    Google Scholar 

  2. Accardi, L., Frigerio, A., and Lu Y.-G.: The weak coupling limit as a quantum functional central limit theorem. To appear in Commun. Math. Phys.

    Google Scholar 

  3. Accardi, L., Frigerio, A., and Lu Y.-G.: The quantum weak coupling limit (II). Langevin equation and finite temperature case. Preprint University of Rome II (1989).

    Google Scholar 

  4. Accardi, L., Frigerio, A., and Lu Y.-G.: On the weak coupling limit for fermions. Preprint University of Rome II (1989).

    Google Scholar 

  5. Accardi, L., and Lu Y.-G.: The low density limit: the boson Fock case. Preprint Centro Matematico Vito Volterra, Rome (1989).

    Google Scholar 

  6. Davies, E.B.: Markovian master equations. Commun. Math. Phys. 39 (1974) 91–110.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Davies, E.B., and Spohn, H.: J. Stat. Phys. 19 (1978) 511–.

    Article  ADS  MathSciNet  Google Scholar 

  8. Dümcke, R.: Convergence of multi-time correlation functions in the weak and singular coupling limits. J. Math. Phys. 24 (1983) 311–315.

    Article  ADS  MathSciNet  Google Scholar 

  9. Dümcke, R.: The low density limit for an N-level system interacting with a free Bose or Fermi gas. Commun.Math.Phys. 97 (1985) 331–359.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Evans, M., and Hudson, R.L.: Multidimensional quantum diffusions. In: Accardi, L., and von Waldenfels, W. (Eds.): Quantum Probability and Applications III (Proceedings, Oberwolfach 1987). Lecture Notes in Mathematics vol. 1303. Springer-Verlag, Berlin Heidelberg New York Tokyo (1988) pp. 69–88.

    Chapter  Google Scholar 

  11. Frigerio, A.: Quantum Poisson processes: physical motivations and applications. In: Accardi, L., and von Waldenfels, W. (Eds.): Quantum Probability and Applications III (Proceedings, Oberwolfach 1987). Lecture Notes in Mathematics vol. 1303. Springer-Verlag, Berlin Heidelberg New York Tokyo (1988) pp. 107–127.

    Chapter  Google Scholar 

  12. Frigerio, A., and Gorini, V.: Markov dilations and quantum detailed balance. Commun. Math. Phys. 93 (1984) 517–532.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Gorini, V., Kossakowski, A., and Sudarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17 (1976) 821–825.

    Article  ADS  MathSciNet  Google Scholar 

  14. Hudson, R.L., and LIndsay, J.M.: A non-commutative martingale representation theorem for non-Fock quantum Brownian motion. J. Funct. Anal. 61 (1985) 202–221.

    Article  MathSciNet  MATH  Google Scholar 

  15. Hudson, R.L., and Lindsay, J.M.: Uses of non-Fock quantum Brownian motion and a martingale representation theorem. In: Accardi, L., and von Waldenfels, W. (Eds.): Quantum Probability and Applications II (Proceedings, Heidelberg 1984). Lecture Notes in Mathematics vol. 1136. Springer-Verlag, Berlin Heidelberg New York Tokyo (1985) pp. 276–305.

    Chapter  Google Scholar 

  16. Hudson, R.L., and Parthasarathy, K.R.: Quantum Ito’s formula and stochastic evolutions. Commun. Math. Phys. 91 (1984) 301–323.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48 (1976) 119–130.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Pulè, J.V.: The Bloch equations. Commun. Math. Phys. 38 (1974) 241–256.

    Article  ADS  MathSciNet  Google Scholar 

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Luigi Accardi Wilhelm von Waldenfels

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© 1990 Springer-Verlag

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Accardi, L., Frigerio, A., Lu, YG. (1990). Quantum Langevin equation in the weak coupling limit. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications V. Lecture Notes in Mathematics, vol 1442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085499

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  • DOI: https://doi.org/10.1007/BFb0085499

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53026-8

  • Online ISBN: 978-3-540-46311-5

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