Local Temperature and Universal Heat Conduction in FPU chains

TL;DR

This paper investigates heat conduction in FPU chains, revealing how local temperature behaves unexpectedly and demonstrating that thermal conductivity diverges with chain length as N^(1/3), contributing to the understanding of universality in 1D heat conduction.

Contribution

It provides numerical evidence of local temperature behavior in FPU chains and clarifies the divergence of thermal conductivity with chain length, addressing longstanding debates.

Findings

Local temperature exhibits paradoxical behavior in steady state.

Thermal conductivity diverges as N^(1/3) with chain length.

Earlier simulations overestimated the divergence exponent.

Abstract

It is shown numerically that for Fermi Pasta Ulam (FPU) chains with alternating masses and heat baths at slightly different temperatures at the ends, the local temperature (LT) on small scales behaves paradoxically in steady state. This expands the long established problem of equilibration of FPU chains. A well-behaved LT appears to be achieved for equal mass chains; the thermal conductivity is shown to diverge with chain length N as N^(1/3), relevant for the much debated question of the universality of one dimensional heat conduction. The reason why earlier simulations have obtained systematically higher exponents is explained.