Download PDF by Vincent Rivasseau (Chief Editor): Annales Henri Poincaré - Volume 4

By Vincent Rivasseau (Chief Editor)

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We will see that our CLT is valid for a dense algebra invariant under the time evolution generated by any finite range translationally invariant Hamiltonian. As a corollary, we can introduce the time evolution for the algebra of normal fluctuation directly. The CLT of this paper implies that quasifree states obtained in CLT is a KMS state of the algebra of fluctuation provided that the microscopic state satisfies the KMS condition as well. We concentrate here on the one-dimensional system. We may derive the same CLT for higher-dimensional systems under a similar mixing assumption of states, though the condition looks rather difficult to verify, so we do not present its proof here.

321, no. 8, 1089–1095 (1995). [5] J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10, no. 1, 1–68 (1978). [6] Helmut Friedrich and Alan Rendall, The Cauchy problem for the Einstein equations, Einstein’s field equations and their physical implications, Springer, Berlin, 2000, pp. 127–223. [7] Mikhael Gromov and H. , Positive scalar curvature and the ´ Dirac operator on complete Riemannian manifolds, Inst. Hautes Etudes Sci. Publ. Math. (1983), no. 58, 83–196 (1984). [8] Tosio Kato, Abstract evolution equations, linear and quasi-linear, revisited, Functional analysis and related topics, 1991 (Kyoto), Springer, Berlin, 1993, pp.

N + m) Λk ∩ Λl = ∅(k = l) and r = min{distance{Λi, Λj } i = j = 1, 2, . . n + m}. The constant C must be independent on n, m and the size of support Λj . D. Goderis, A. Verbeure, and P. Vets never proved their assumption for any (non-product ) Gibbs state and until recently it has been an open question whether the above results really hold for any Gibbs states. In [12], we obtained a different proof of CLT of a single observable in quantum spin systems under a slightly different mixing condition.

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Annales Henri Poincaré - Volume 4 by Vincent Rivasseau (Chief Editor)


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