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arXiv:0908.3441 · Journal of the Physical Society of Japan

General Properties of Response Functions of Nonequilibrium Steady States

Akira Shimizu, Tatsuro Yuge

Published Jan 12, 2010• 23 citations
arXivHTMLPDF

Abstract

We derive general properties, which hold for both quantum and classical systems, of response functions of nonequilibrium steady states. We clarify differences from those of equilibrium states. In particular, sum rules and asymptotic behaviors are derived, and their implications are discussed. Since almost no assumptions are made, our results are applicable to diverse physical systems. We also demonstrate our results by a molecular dynamics simulation of a many-body interacting system.

DOI
10.1143/jpsj.79.013002

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The fluctuations of macroscopic observables in quantum systems which are in a nonequilibrium steady state are studied rigorously in the thermodynamic limit. In particular, the nonequilibrium steady state (NESS) of a quantum spin system that is composed of two infinite reservoirs at different temperatures coupled in a bounded region is considered. Under suitable assumptions on the interaction and the asymptotics of the fluctuations, a nonequilibrium central limit theorem for the fluctuations of the NESS expectation value of the empirical average of observables is proven by showing the analyticity of the corresponding moment generating function in a neighbourhood of the origin using the cluster expansion method. Furthermore, the large deviation principle is proven for a class of observables by establishing the existence and differentiability of the corresponding moment generating function.