Thermal conductivity of the Toda lattice with conservative noise

TL;DR

This paper investigates how stochastic noise affects heat transport in the Toda lattice, revealing that the thermal conductivity diverges with system size and depends on noise strength, indicating anomalous heat conduction.

Contribution

It demonstrates that stochastic perturbations induce anomalous thermal conductivity in the Toda lattice, with a divergence exponent depending on noise intensity.

Findings

Thermal conductivity diverges as a power law with system size.

The divergence exponent varies with noise strength.

Ballistic conduction in the unperturbed Toda lattice is suppressed.

Abstract

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter $\gamma$. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length $n$ of the chain according to $\kappa(n) \sim n^\alpha$, with $0 < \alpha \leq 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $\alpha$ of the divergence depends on $\gamma$.