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Multiple phases and return to equilibrium

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Abstract

This paper considers the problem of return to equilibrium for perturbations of the dynamics of the one-sided and two-sidedXY-models with external field. We find that, in the presence of multiple ground states, return to equilibrium fails for certain perturbations while still holding wen there is a unique ground state.

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References

  1. Huzihiro Araki and Eytan Barouch, On the dynamics and ergodic properties of theXY model,J. Stat. Phys. 31:327–345 (1983).

    Google Scholar 

  2. D. B. Abraham, E. Barouch, G. Gallavotti, and A. Martin-Löf, Dynamics of a local perturbation in theXY model I—Approach to equilibrium,Stud. Appl. Math. 50:121–131 (1971).

    Google Scholar 

  3. D. B. Abraham, E. Barouch, G. Gallavotti, and A. Martin-Löf, Dynamics of a local perturbation in theXY model II—Excitations,Stud. Appl. Math. 51:211–218 (1972).

    Google Scholar 

  4. Huzihiro Araki and Taku Matsui, Ground states of theXY-model,Commun. Math. Phys. 101:213–245 (1986).

    Google Scholar 

  5. Huzihiro Araki, On theXY-model on two-sided infinite chain,Publ. RIMS Kyoto Univ. 20:277–296 (1984).

    Google Scholar 

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

    Google Scholar 

  7. Huzihiro Araki, On quasi-free states of CAR and Bogoliubov automorphism,Publ. RIMS Kyoto Univ. 6:385–442 (1970).

    Google Scholar 

  8. Ola Bratteli and Derek W. Robinson,Operator Algebras and Quantum Statistical Mechanics II (Springer-Verlag, New York, 1981).

    Google Scholar 

  9. William Fulton,Algebraic Curves: An Introduction to Algebraic Geometry (Benjamin, Reading Massachusetts, 1969).

    Google Scholar 

  10. Leigh R. Hume and Derek W. Robinson, Return to equilibrium in theXY-model,J. Stat. Phys. 44:829–848 (1986).

    Google Scholar 

  11. Keith Kendig,Elementary Algebraic Geometry (Springer-Verlag, New York, 1977).

    Google Scholar 

  12. Michael Reed and Barry Simon,Methods of Modern Mathematical Physics IV: Analysis of Operators (Academic Press, London, 1978).

    Google Scholar 

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Authors and Affiliations

  1. School of Information Science and Technology, Flinders University of South Australia, Australia

    A. L. Carey & L. R. Hume

  2. Department of Mathematics, School of MPCE, Macquarie University, Australia

    A. L. Carey & L. R. Hume

Authors
  1. A. L. Carey
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  2. L. R. Hume
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Carey, A.L., Hume, L.R. Multiple phases and return to equilibrium. J Stat Phys 68, 787–828 (1992). https://doi.org/10.1007/BF01048876

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  • DOI: https://doi.org/10.1007/BF01048876

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