Thermal conductivity of the Toda lattice with conservative noise

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 $0<\alpha \le 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $\alpha$ of the divergence depends on $\gamma$.

References in corpus (3)

• A momentum conserving model with anomalous thermal conductivity in low dimension
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs

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• Thermal transport in long-range interacting harmonic chains perturbed by long-range conservative noise
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise
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