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Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior

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Abstract

An overview is given of the long-time and long-distance behavior of correlation functions in both classical and quantum statistical mechanics. After a simple derivation of the classical long-time tails in equilibrium time correlation functions, we discuss analogous long-distance phenomena in nonequilibrium classical systems. The paper then draws analogies between these phenomena and similar effects in quantum statistical mechanics, with emphasis on the soft modes that underly long-time tails and related phenomena. We also elucidate the interplay between critical phenomena and long-time tails, using the classical liquid-gas critical point and the quantum ferromagnetic transition as examples.

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Authors and Affiliations

  1. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland, 20742

    T. R. Kirkpatrick & J. V. Sengers

  2. Department of Physics, University of Maryland, College Park, Maryland, 20742

    T. R. Kirkpatrick

  3. Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon, 97403

    D. Belitz

  4. Department of Chemical Engineering, University of Maryland, College Park, Maryland, 20742

    J. V. Sengers

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Kirkpatrick, T.R., Belitz, D. & Sengers, J.V. Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior. Journal of Statistical Physics 109, 373–405 (2002). https://doi.org/10.1023/A:1020485809093

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