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Correlations and scaling in one-dimensional heat conduction

J. M. Deutsch·Onuttom Narayan
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Abstract

We examine numerically the full spatio-temporal correlation functions for all hydrodynamic quantities for the random collision model introduced recently. The autocorrelation function of the heat current, through the Kubo formula, gives a thermal conductivity exponent of 1/3 in agreement with the analytical prediction and previous numerical work. Remarkably, this result depends crucially on the choice of boundary conditions: for periodic boundary conditions (as opposed to open boundary conditions with heat baths) the exponent is approximately 1/2. This is expected to be a generic feature of systems with singular transport coefficients. All primitive hydrodynamic quantities scale with the dynamic critical exponent predicted analytically.

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J. M. Deutsch, Onuttom Narayan. 2003-06-04. Correlations and scaling in one-dimensional heat conduction. https://doi.org/10.1103/physreve.68.041203

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