Large deviations of heat flow in harmonic chains

Abstract

We consider heat transport across a harmonic chain connected at its two ends to white-noise Langevin reservoirs at different temperatures. In the steady state of this system the heat $Q$ flowing from one reservoir into the system in a finite time $\tau$ has a distribution $P(Q,\tau )$. We study the large time form of the corresponding moment generating function $<e^{-\lambda Q}>\sim g(\lambda )e^{\tau \mu (\lambda )}$. Exact formal expressions, in terms of phonon Green's functions, are obtained for both $\mu (\lambda )$ and also the lowest order correction $g(\lambda )$. We point out that, in general a knowledge of both $\mu (\lambda )$ and $g(\lambda )$ is required for finding the large deviation function associated with $P(Q,\tau )$. The function $\mu (\lambda )$ is known to be the largest eigenvector of an appropriate Fokker-Planck type operator and our method also gives the corresponding eigenvector exactly.

15 pages; minor modifications

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