On the universality of anomalous one-dimensional heat conductivity

TL;DR

This paper investigates the divergence of heat conductivity in one-dimensional systems, showing that numerical results deviate from the previously predicted theoretical exponent, indicating a potential universality issue.

Contribution

The study provides extensive numerical evidence that the heat conductivity exponent in 1D chains differs from the theoretical prediction, challenging existing universality assumptions.

Findings

Finite-size thermal conductivity diverges as L^α

Numerical exponent α systematically deviates from 1/3

Results suggest possible universality breakdown in 1D heat transport

Abstract

In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long--time correlation of the corresponding currents. The effective asymptotic behaviour is addressed with reference to the problem of heat transport in 1d crystals, modeled by chains of classical nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium numerical simulations confirm that the finite-size thermal conductivity diverges with the system size $L$ as $\kappa \propto L^\alpha$. However, the exponent $\alpha$ deviates systematically from the theoretical prediction $\alpha=1/3$ proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev. Lett. {\bf 89}, 200601 (2002)].