Correlations and scaling in one-dimensional heat conduction

We examine numerically the full spatiotemporal 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 $\approx 1/2.$ All primitive hydrodynamic quantities scale with the dynamic critical exponent predicted analytically.