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Operator algebras in statistical mechanics and noncommutative probability theory

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Abstract

The fundamental notions of statistical mechanics of quantum spin systems are introduced. A survey of the main properties of the states satisfying the Kubo-Martin-Schwinger boundary conditions is given. The problem of describing the invariant states and the first integrals for the multidimensional Heisenberg model is solved. A central limit theorem of noncommutative probability theory and a noncommutative analog of the individual ergodic theorem are formulated and proved. The asymptotics of the distribution of the eigenvalues of the multiparticle Schrodinger operator is studied.

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Authors
  1. V. V. Anshelevich
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  2. M. Sh. Gol'dshtein
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki (Noveishie Dostizheniya), Vol. 27, pp. 191–228, 1985.

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Anshelevich, V.V., Gol'dshtein, M.S. Operator algebras in statistical mechanics and noncommutative probability theory. J Math Sci 37, 1523–1553 (1987). https://doi.org/10.1007/BF01103857

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