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Abstract

We generalize the classical notion of aK-system to a non-commutative dynamical system by requiring that an invariantly defined memory loss be 100%. We give some examples of quantumK-systems and show that they cannot contain any quasi-periodic subsystem.

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References

  1. Arnold, V. J., Avez, A.: Problèmes Ergodiques de la Mecanique classique. Paris: Gauthier Villars 1967

    Google Scholar 

  2. Emch, G. G.: Commun. Math. Phys.49, 191 (1976)

    Google Scholar 

  3. Kümmerer, B., Schröder, W.: Commun. Math. Phys.90, 251 (1983)

    Google Scholar 

  4. Schröder, W.: In: Quantum probability and applications to the quantum theory of irreversible processes, p. 340. Accardi, L., Frigerio, A., Gorini, V. (eds.). Berlin, Heidelberg, New York: Springer 1984

    Google Scholar 

  5. Connes, A., Narnhofer, H., Thirring, W.: Commun. Math. Phys.112, 691 (1987)

    Google Scholar 

  6. Verbeure, A.: private communication

  7. Krieger, W.: Trans. Am. Math. Soc.149, 453 (1970)

    Google Scholar 

  8. Narnhofer, H., Thirring, W.: Mixing properties of quantum systems, Vienna preprint UWTHPh 1988-18

  9. Thirring, W.: Klassische dynamische Systeme (2.6.13, 4), 2. ed. Wien: Springer 1988

    Google Scholar 

  10. Narnhofer, H., Thirring, W.: Lett. Math. Phys.14, 89 (1987)

    Google Scholar 

  11. Powers, R. T.: Ann. Math.86, 138 (1967)

    Google Scholar 

  12. Cornfeld, P., Fomin, S. V., Sinai, Ya. G.: Ergodic theory. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  13. Rohlin, V. A.: Lectures on ergodic theory. Russ. Math. Surv.22, (1967)

  14. Narnhofer, H.: Vienna preprint UWThPh-1989-3, to be published

  15. Hudetz, T.: Lett. Math. Phys.16, 151 (1988)

    Google Scholar 

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Communicated by Ya. G. Sinai

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Narnhofer, H., Thirring, W. QuantumK-systems. Commun.Math. Phys. 125, 565–577 (1989). https://doi.org/10.1007/BF01228341

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  • DOI: https://doi.org/10.1007/BF01228341

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