Heat conduction in the \alpha-\beta -Fermi-Pasta-Ulam chain

TL;DR

This paper investigates heat conduction in a one-dimensional - Fermi-Pasta-Ulam chain, revealing that previous findings of normal heat transport were due to finite-size effects, and that the true asymptotic behavior remains anomalous.

Contribution

The study provides detailed numerical simulations showing that the observed normal heat conduction is a finite-size effect, clarifying the asymptotic behavior of the system.

Findings

Finite chain length affects heat conduction results.

Asymptotic behavior remains anomalous despite finite-size observations.

No evidence of a finite temperature phase transition.

Abstract

Recent simulation results on heat conduction in a one-dimensional chain with an asymmetric inter-particle interaction potential and no onsite potential found non-anomalous heat transport in accordance to Fourier's law. This is a surprising result since it was long believed that heat conduction in one-dimensional systems is in general anomalous in the sense that the thermal conductivity diverges as the system size goes to infinity. In this paper we report on detailed numerical simulations of this problem to investigate the possibility of a finite temperature phase transition in this system. Our results indicate that the unexpected results for asymmetric potentials is a result of insufficient chain length, and does not represent the asymptotic behavior.