Thermal conductivity for a chain of anharmonic oscillators perturbed by a conservative noise

TL;DR

This paper reviews the thermal conduction properties of d-dimensional chains of anharmonic oscillators perturbed by energy- or energy-and-momentum-conserving noise, highlighting key results and open questions.

Contribution

It provides a comprehensive review of the thermal conduction behavior in such stochastic oscillator chains, including recent findings and unresolved issues.

Findings

Thermal conductivity behaviors depend on the type of noise and system dimensionality.

Certain noise perturbations lead to anomalous heat transport.

Open questions remain on the precise mechanisms governing thermal conduction in these models.

Abstract

We consider $d$-dimensional chains of (an)harmonic oscillators we perturb by a noise conserving energy or energy and momentum. We review the thermal conduction properties we obtained for these systems and conclude by several open questions.