Correlations and scaling in one-dimensional heat conduction

TL;DR

This paper numerically investigates one-dimensional heat conduction, revealing how boundary conditions affect the thermal conductivity exponent and confirming the scaling of hydrodynamic quantities with predicted critical exponents.

Contribution

It demonstrates the impact of boundary conditions on the thermal conductivity exponent and confirms the scaling behavior of hydrodynamic quantities in a one-dimensional model.

Findings

Thermal conductivity exponent is 1/3 with open boundaries.

Exponent is approximately 1/2 with periodic boundaries.

Hydrodynamic quantities scale with analytically predicted critical exponents.

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.