Heat conduction in the disordered Fermi-Pasta-Ulam chain

TL;DR

This paper investigates how disorder affects heat conduction in an anharmonic FPU chain, finding no finite-temperature transition and confirming the usual size dependence of thermal current, with new insights into the binary-mass ordered case.

Contribution

It provides a detailed analysis showing disorder does not induce a finite thermal conductivity transition, and extends understanding to binary-mass ordered FPU chains.

Findings

Disorder does not lead to a finite-temperature transition in heat conduction.

At low temperatures, transport is dominated by disorder in small systems.

Asymptotic current scales as J ~ 1/N^{2/3} in the FPU chain.

Abstract

We address the question of the effect of disorder on heat conduction in an anharmonic chain with interactions given by the Fermi-Pasta-Ulam (FPU) potential. In contrast to the conclusions of an earlier paper [Phys. Rev. Lett. 86, 63 (2001)] which found that disorder could induce a finite thermal conductivity at low temperatures, we find no evidence of a finite temperature transition in conducting properties. Instead, we find that at low temperatures, small system size transport properties are dominated by disorder but the asymptotic system size dependence of current is given by the usual FPU result J ~ 1/N^{2/3}. We also present new interesting results on the binary-mass ordered FPU chain.