Large deviations of heat flow in harmonic chains

Details Large deviations of heat flow in harmonic chains Large deviations of heat flow in harmonic chains

2011-01-19

arxiv.org/abs/1101.3669v2

J. Stat. Mech. (2011) P03007

Physics

Condensed Matter

Statistical Mechanics

15 pages; minor modifications

Scientific paper

10.1088/1742-5468/2011/03/P03007

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 $\sim g(\lambda) e^{\tau\mu (\lambda)}$. 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.

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