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

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

2001-10-29

arxiv.org/abs/cond-mat/0110603v1

J. Stat. Phys. 109, 373 (2002)

Physics

Condensed Matter

Statistical Mechanics

15 pp., REVTeX, 8 ps figs

Scientific paper

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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