Abhishek Dhar, Keiji Saito, Bernard Derrida
The Levy-walk model is known to provide a good description of anomalous heat conduction in one-dimensional systems. In this model the heat carriers execute Levy-walks instead of normal diffusion as expected in systems where Fourier's law holds. Here we calculate exactly the average heat current, the large deviation function of its fluctuations and the temperature profile of the Levy-walk model maintained in a steady state by contact with two heat baths (the open geometry). We find that the current is nonlocally connected to the temperature gradient. As observed in recent simulations of mechanical models, all the cumulants of the current fluctuations have the same system-size dependence in the open geometry. The case of the ring geometry is also discussed.
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http://arxiv.org/abs/1207.1184
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