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Ergodic properties of some C*-dynamical systems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1132)

Abstract

Return to equilibrium in the one-dimensional XY-model is discussed with emphasis on mathematical aspect. A related mathematical structure is discussed also in connection with the two-dimensional Ising model, especially using ℤ2-index for two projections.

Keywords

  • Ergodic Property
  • Cyclic Representation
  • Integral Decomposition
  • Unique Equilibrium State
  • Quantum Lattice System

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References

  1. H. Araki, On the algebra of all local observables, Progr. Theoret. Phys. 32 (1964), 844–854.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. H. Araki, On quasifree states of CAR and Bogoliubov automorphisms, Publ. RIMS Kyoto Univ. 6 (1970), 384–442.

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  3. H. Araki, On uniqueness of KMS states of one-dimensional quantum lattice systems, Commun. Math. Phys. 44 (1975), 1–7.

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  4. H. Araki and E. Barouch, On the dynamical and ergodic properties of the XY model, J. Stat. Phys. 31 (1983), 327–345.

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  5. H. Araki, On the XY-model on two-sided infinite chain, RIMS preprint 435. To appear in Publ. RIMS Kyoto Univ. 20 (1984), No.2.

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  6. H. Araki and D. E. Evans, On a C*-algebra approach to phase transition in the two-dimensional Ising model, to appear in Commun. Math. Phys.

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  7. O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics II, Springer, 1981.

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  8. A. Kishimoto, Dissipations and derivations, Commun. Math. Phys. 47 (1976), 167–170.

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  9. D. W. Robinson, Return to equilibrium, Commun. Math. Phys. 31 (1973), 171–189.

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© 1985 Springer-Verleg

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Araki, H. (1985). Ergodic properties of some C*-dynamical systems. In: Araki, H., Moore, C.C., Stratila, ŞV., Voiculescu, DV. (eds) Operator Algebras and their Connections with Topology and Ergodic Theory. Lecture Notes in Mathematics, vol 1132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074874

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  • DOI: https://doi.org/10.1007/BFb0074874

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15643-7

  • Online ISBN: 978-3-540-39514-0

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