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The Green-Kubo Formula and the Onsager Reciprocity Relations in Quantum Statistical Mechanics

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Abstract

We study linear response theory in the general framework of algebraic quantum statistical mechanics and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Our derivation is axiomatic and the key assumptions concern ergodic properties of non-equilibrium steady states.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada

    V. Jakšić

  2. CPT-CNRS, UMR 6207, Université du Sud, Toulon-Var, B.P. 20132, 83957, La Garde Cedex, France

    Y. Ogata & C. A. Pillet

  3. Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153-8914, Japan

    Y. Ogata

Authors
  1. V. Jakšić
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  2. Y. Ogata
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  3. C. A. Pillet
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Dedicated to David Ruelle on the occasion of his 70th birthday.

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Jakšić, V., Ogata, Y. & Pillet, C.A. The Green-Kubo Formula and the Onsager Reciprocity Relations in Quantum Statistical Mechanics. Commun. Math. Phys. 265, 721–738 (2006). https://doi.org/10.1007/s00220-006-0004-6

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  • DOI: https://doi.org/10.1007/s00220-006-0004-6

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