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Dilations of quantum dynamical semigroups with classical Brownian motion

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Abstract

We show that any quantum dynamical semigroup can be written with the help of the solution of a vector-valued classical stochastic differential equation. Moreover this equation leads to a natural construction of a unitary dilation in term of Wiener spaces.

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References

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

    Google Scholar 

  2. Gorini, V., Kossakowski, A., Sudarshan, E. C. G.: Completely positive dynamical semigroups ofN-level systems. J. Math. Phys.17, 821 (1976)

    Google Scholar 

  3. Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys.48, 119 (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.13, 149 (1978)

    Google Scholar 

  5. Evans, D. E., Lewis, J. T.: Dilations of irreversible evolutions in algebraic quantum theory. Commun. Dublin Inst. Adv. Study24, Ser. A (1977)

  6. Kümmerer, B.: A dilation theory for completely positive operators onW*-algebras, Thesis, Tübingen (1982)

  7. Accardi, L., Frigerio, A., Gorini, V., (eds.): Quantum probability and applications to the quantum theory of irreversible processes, Lecture Notes in Mathematics Vol.1055, Berlin, Heidelberg, New York: Springer 1984

    Google Scholar 

  8. Accardi, L., von Waldenfels, W. (eds.): Quantum probability and applications II, Lecture Notes in Mathematics Vol.1136, Berlin, Heidelberg, New York: Springer 1985

    Google Scholar 

  9. Barnett, C., Streater, R.F., Wilde, I.: J. Funct. Anal.48, 172 (1982)

    Google Scholar 

  10. Hudson, R. L., Parthasarathy, K. R.: Time-orthogonal unitary dilations and non-commutative Feynman-Kac formulae. Commun. Math. Phys.83, 301 (1984)

    Google Scholar 

  11. Applebaum, D. B., Hudson, R. L.: Fermion Ito's formula and stochastic evolutions. Commun. Math. Phys.96, 473 (1984)

    Google Scholar 

  12. Alicki, R., Fannes, M.: On dilating quantum dynamical semigroups with classical brownian motion, Leuven preprint KUL-TF-85/17

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Authors and Affiliations

  1. Instituut voor Theoretische Fysica, Universiteit Leuven, B-3030, Leuven, Belgium

    R. Alicki & M. Fannes

Authors
  1. R. Alicki
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  2. M. Fannes
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Additional information

Communicated by H. Araki

On leave of absence from Institute of Theoretical Physics and Astrophysics, Gdansk, Poland

Bevoegdverklaard navorser N.F.W.O., Belgium

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Alicki, R., Fannes, M. Dilations of quantum dynamical semigroups with classical Brownian motion. Commun.Math. Phys. 108, 353–361 (1987). https://doi.org/10.1007/BF01212314

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  • DOI: https://doi.org/10.1007/BF01212314

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