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On the equivalence of KMS and Gibbs conditions for states of quantum lattice systems

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Abstract

The equivalence of a Gibbsian equilibrium condition and the KMS condition is proven for one-dimensional quantum lattice systems with a finite range interaction at arbitrary temperature, and for quantum lattice systems of arbitrary dimension, with a finite body interaction, at high temperature.

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References

  1. Araki, H.: Publ. RIMS4A, 361–371 (1968)

    Google Scholar 

  2. Araki, H.: Commun. math. Phys.14, 120–157 (1969)

    Google Scholar 

  3. Araki, H.: Ann. Sci. École Norm. Sup.6, 67–84 (1973)

    Google Scholar 

  4. Araki, H.: Preprint RIMS 120. To appear in Pacific J. Math.

  5. Araki, H.: Publ. RIMS9, 165–209 (1973)

    Google Scholar 

  6. Brascamp, H. J.: Commun. math. Phys.18, 82–96 (1970)

    Google Scholar 

  7. Dobrushin, R. L.: Theor. Prob. Appl.12 (4), 535–559 (1967); — Teor. Veroyatnost Primen.12, 595–618 (1967)

    Google Scholar 

  8. Dobrushin, R. L.: Funkcional. Anal. i Priložen.2 (4), 31–43 (1968); — Functional Anal. Appl.2, 292–301 (1968)

    Google Scholar 

  9. Lanford III, O. E., Robinson, D. W.: J. Math. Phys.9, 1120–1125 (1968)

    Google Scholar 

  10. Lanford III, O. E., Robinson, D. W.: Commun. math. Phys.9, 327–338 (1968)

    Google Scholar 

  11. Lanford III, O. E., Ruelle, D.: Commun. math. Phys.13, 194–215 (1969)

    Google Scholar 

  12. Powers, R. T.: Ann. Math.86 (1), 138–171 (1967)

    Google Scholar 

  13. Robinson, D. W.: Commun. math. Phys.7, 337–348 (1968)

    Google Scholar 

  14. Ruelle, D.: Statistical Mechanics, New York-Amsterdam: Benjamin 1969

    Google Scholar 

  15. Streater, R. F.: Commun. math. Phys.6, 233–247 (1967)

    Google Scholar 

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    Huzihiro Araki & P. D. F. Ion

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  1. Huzihiro Araki
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  2. P. D. F. Ion
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Araki, H., Ion, P.D.F. On the equivalence of KMS and Gibbs conditions for states of quantum lattice systems. Commun.Math. Phys. 35, 1–12 (1974). https://doi.org/10.1007/BF01646450

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  • DOI: https://doi.org/10.1007/BF01646450

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