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arXiv:hep-th/9809016 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Generalized fluctuation-dissipation theorem for nonlinear response functions

Enke Wang, Ulrich Heinz

Published Jul 2, 2002• 122 citations
arXivHTMLPDF

Abstract

A nonlinear generalization of the fluctuation-dissipation theorem (FDT) for the n-point Green functions and the amputated one particle irreducible vertex functions at finite temperature is derived in the framework of the closed time path formalism. We verify that this generalized FDT coincides with known results for $n=2$ and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.

DOI
10.1103/physrevd.66.025008

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A nonlinear generalization of the fluctuation-dissipation theorem (FDT) for the n-point Green functions and the amputated one particle irreducible vertex functions at finite temperature is derived in the framework of the closed time path formalism. We verify that this generalized FDT coincides with known results for n=2n=2n=2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.
Based on the closed time path formalism, a new Feynman rule for directly calculating the retarded and advanced Green functions is deduced. This Feynman rule is used to calculate the two-point self-energy and three-point vertex correction in ϕ3ϕ^3ϕ3 theory. The generalized fluctuation-dissipation theorem for three-point nonlinear response function is verified.
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There is no simple fluctuation-dissipation theorem (FDT) for nonequilibrium systems. We show that for a fluid in a nonequilibrium steady state (NESS) characterized by a constant temperature gradient there is a generalized FDT that relates commutator correlation functions to the bilinear response of products of observables. This allows for experimental probes of the long-range correlations in such a system, quantum or classical, via response experiments. We also show that the correlations are not tied to thermal fluctuations but are intrinsic to the NESS and reflect a generalized rigidity.
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