Abstract
The time development of quantum lattice systems is studied without any restrictions on the growth condition of the potential Φ. A thermodynamic limit ω of quantum Gibbs state, a *-algebra \(\mathcal{W} \) and an automorphism group αt for which ω is a KMS state are constructed.
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References
Borchers, H. J.: Nuovo Cim. 24 (1962), 214.
Brüning, E. and Nagamachi, S.: J. Math. Phys. 30 (1989), 2340.
Davis, M.: Applied Nonstandard Analysis, Wiley-Interscience, New York, 1977.
Dubin, D. A. and Sewell, G. L.: J. Math. Phys. 11 (1970), 2990.
Hille, E. and Phillips, R. S.: Functional Analysis and Semi-group, Amer. Math. Soc., Providence, Rhode Island, 1957.
Kaneko, A.: Introduction to Hyperfunctions, Kluwer Academic Publ., Dordrecht, Boston, London, 1988.
Nagamachi, S. and Mugibayashi, N.: Comm. Math. Phys. 46 (1976), 119.
Nagamachi, S. and Nishimura, T.: Funkcialaj Ekvacioj 36 (1993), 499.
Ojima, I.: Ann. Phys. 137 (1981), 1.
Ruelle, D.: Statistical Mechanics, Benjamin, New York, Amsterdam, 1969.
Ruskai, M. B.: Comm. Math. Phys. 20 (1971), 193.
Streater, R. F. and Wightman, A. S.: PCT, Spin and Statistics and All That, Benjamin, New York, Amsterdam, 1964.
Tillmann, H.-G.: Math. Zeit. 59 (1953), 61.
Treves, F.: Topological Vector Spaces, Distributions and Kernels, Academic Press, New York, 1967.
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Nagamachi, S. A Note on the Time Development of Quantum Lattice Systems. Letters in Mathematical Physics 39, 163–178 (1997). https://doi.org/10.1023/A:1007320903571
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DOI: https://doi.org/10.1023/A:1007320903571