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Cecchini's transition expectations and markov chains

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Quantum Probability and Applications IV

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1396))

Abstract

Heuristically a quantum Markov chain indexed by N is a state ϕ on ⊗N B (Ba matrix algebra) whose sequence of density matrices has a local structure (corresponding to the physical intuition that the interaction Hamiltonian is nearest neighbour). In [1] two classes of such chains were constructed: the Markov chains and the generalized Markov chains. In

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Bibliography

  1. Accardi L., Noncommutative Markov chains. In: international School of Mathematical Physics, Camerino (1974) 268–295.

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  2. Accardi L. Topics in Quantum Probability Physics Reports, 77(1981)169–192

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  3. Accardi L., A. Frigerio, J.T. Lewis, Quantum stochastic processes Publications of the Research institute for Mathematical Sciences Kyoto University 18 (1982) 97–133).

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  4. Accardi L., A. Frigerio, Markovian cocycles Proc. Royal Irish Acad. 83A (1983) 251–263.

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  5. Cecchini C., Stochastic couplings for von Neumann algebras. cf. these proceedings.

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Luigi Accardi Wilhelm von Waldenfels

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© 1989 Springer-Verlag

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Accardi, L. (1989). Cecchini's transition expectations and markov chains. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications IV. Lecture Notes in Mathematics, vol 1396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083540

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  • DOI: https://doi.org/10.1007/BFb0083540

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51613-2

  • Online ISBN: 978-3-540-46713-7

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