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Multiple phases and return to equilibrium. (English) Zbl 0889.46060

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

MSC:

46N55 Applications of functional analysis in statistical physics
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
Full Text: DOI

References:

[1] Huzihiro Araki and Eytan Barouch, On the dynamics and ergodic properties of theXY model,J. Stat. Phys. 31:327-345 (1983). · Zbl 0591.58019 · doi:10.1007/BF01011585
[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).
[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).
[4] Huzihiro Araki and Taku Matsui, Ground states of theXY-model,Commun. Math. Phys. 101:213-245 (1986). · Zbl 0581.46058 · doi:10.1007/BF01218760
[5] Huzihiro Araki, On theXY-model on two-sided infinite chain,Publ. RIMS Kyoto Univ. 20:277-296 (1984). · Zbl 0544.46040 · doi:10.2977/prims/1195181608
[6] Huzihiro Araki, On uniqueness of KMS states of one-dimensional quantum lattice systems,Commun. Math. Phys. 44:1-7 (1975). · Zbl 0309.46054 · doi:10.1007/BF01609054
[7] Huzihiro Araki, On quasi-free states of CAR and Bogoliubov automorphism,Publ. RIMS Kyoto Univ. 6:385-442 (1970). · Zbl 0227.46061 · doi:10.2977/prims/1195193913
[8] Ola Bratteli and Derek W. Robinson,Operator Algebras and Quantum Statistical Mechanics II (Springer-Verlag, New York, 1981). · Zbl 0463.46052
[9] William Fulton,Algebraic Curves: An Introduction to Algebraic Geometry (Benjamin, Reading Massachusetts, 1969). · Zbl 0681.14011
[10] Leigh R. Hume and Derek W. Robinson, Return to equilibrium in theXY-model,J. Stat. Phys. 44:829-848 (1986). · Zbl 0632.46071 · doi:10.1007/BF01011909
[11] Keith Kendig,Elementary Algebraic Geometry (Springer-Verlag, New York, 1977).
[12] Michael Reed and Barry Simon,Methods of Modern Mathematical Physics IV: Analysis of Operators (Academic Press, London, 1978). · Zbl 0401.47001
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