PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1998 | 43 | 1 | 241-251
Tytuł artykułu

Quantum dynamical entropy revisited

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We define a new quantum dynamical entropy for a C*-algebra automorphism with an invariant state (and for an appropriate 'approximating' subalgebra), which entropy is a 'hybrid' of the two alternative definitions by Connes, Narnhofer and Thirring resp. by Alicki and Fannes (and earlier, Lindblad). We report on this entropy's properties and on three examples.
Słowa kluczowe
Rocznik
Tom
43
Numer
1
Strony
241-251
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Institute of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria
Bibliografia
  • [1] R. Alicki and M. Fannes, Defining Quantum Dynamical Entropy, Lett. Math. Phys. 32 (1994), 75-82.
  • [2] R. Alicki, J. Andries, M. Fannes and P. Tuyls, An Algebraic Approach to the Kolmogorov-Sinai Entropy, Rev. Math. Phys. 8 (2) (1996), 167-184.
  • [3] R. Alicki, D. Makowiec, W. Miklaszewski, Quantum Chaos in Terms of Entropy for the Periodically Kicked Top, Phys. Rev. Lett. 77 (1996), 838-841.
  • [4] R. Alicki and H. Narnhofer, Comparison of Dynamical Entropies for the Noncommutative Shifts, Lett. Math. Phys. 33 (1995), 241-247.
  • [5] J. Andries, M. Fannes, P. Tuyls and R. Alicki, The Dynamical Entropy of the Quantum Arnold Cat Map, Lett. Math. Phys. 35 (1995), 375-383.
  • [6] F. Benatti, T. Hudetz and A. Knauf, Quantum Chaos and Dynamical Entropy, preprint no. 268, SFB 288, TU Berlin, June 1997 (submitted).
  • [7] O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. I / Vol. II (2nd ed.), Springer, New York/Heidelberg/Berlin, 1981/1987.
  • [8] A. Connes, H. Narnhofer and W. Thirring, Dynamical Entropy of C* Algebras and von Neumann Algebras, Commun. Math. Phys. 112 (1987), 691-719.
  • [9] A. Connes and E. Størmer, Entropy for Automorphisms of $II_1$ von Neumann Algebras, Acta Math. 134 (1975), 289-306.
  • [10] V. Ya. Golodets and E. Størmer: Entropy of C*-Dynamical Systems Defined by Bitstreams, preprint no. 18, Dept. of Mathematics, Univ. of Oslo, August 1996.
  • [11] T. Hudetz, A `Hybrid' State-Dependent Dynamical Entropy for C*-Algebra Automorphisms, preprint, Univ. of Vienna (to be submitted).
  • [12] A. N. Kolmogorov, A New Metric Invariant of Transitive Systems and Automorphisms of Lebesgue Spaces, Dokl. Akad. Nauk SSSR 119 (1958), 861-864. Ya. G. Sinai, On the Concept of Entropy of a Dynamical System, Dokl. Akad. Nauk SSSR 124 (1959), 768-771.
  • [13] H. Narnhofer, E. Størmer and W. Thirring, C* Dynamical Systems for Which the Tensor Product Formula for Entropy Fails, Ergod. Th. & Dynam. Sys. 15 (1995), 961-968.
  • [14] H. Narnhofer and W. Thirring, C*-Dynamical Systems that Asymptotically are Highly Anticommutative, Lett. Math. Phys. 35 (1995), 145-154.
  • [15] G. Lindblad, Dynamical Entropy for Quantum Systems, in: Quantum Probability and Applications Vol. III, L. Accardi and W. von Waldenfels (eds.), Springer LNM 1303, Berlin, 1988, pp. 183-191.
  • [16] M. Ohya and D. Petz, Quantum Entropy and Its Use, Springer Texts and Monographs in Physics, Berlin/Heidelberg/New York, 1993.
  • [17] R. T. Powers and G. L. Price, Binary Shifts on the Hyperfinite $II_1$ Factor, Contemporary Math. 145 (1993), 453-464.
  • [18] R. T. Powers and G. L. Price, Cocycle Conjugacy Classes of Shifts on the Hyperfinite $II_1$ Factor, J. Funct. Anal. 121 (1994), 275-295.
  • [19] G. L. Price, The Entropy of Rational Powers Shifts, preprint, Department of Mathematics, United States Naval Academy (Annapolis, Maryland), 1996.
  • [20] E. Størmer and D. Voiculescu, Entropy of Bogoliubov Automorphisms of the Canonical Anticommutation Relations, Commun. Math. Phys. 133 (1990), 521-542.
  • [21] P. Tuyls, Towards Quantum Kolmogorov-Sinai Entropy, Ph.D. Thesis, Univ. Leuven, 1997. Quantization: Non-commutative Dynamical Entropy, Rep. Math. Phys. 38 (1996), 437-442.
  • [22] D. V. Voiculescu, Dynamical Approximation Entropies and Topological Entropy in Operator Algebras, Commun. Math. Phys. 170 (1995), 249-281.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv43i1p241bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.