Numerical analysis of heat transport in classical one-dimensional systems

TL;DR

This paper investigates heat transport in one-dimensional systems, showing that heat conductivity diverges asymptotically, with a focus on models where anomalous hydrodynamic effects dominate at large scales.

Contribution

It demonstrates that in various 1D models, the divergence of heat conductivity is inevitable and introduces a hydrodynamic approach to understand the crossover to anomalous transport regimes.

Findings

Heat conductivity diverges asymptotically in studied models.

Anomalous hydrodynamic contributions dominate at large system sizes.

Crossover to anomalous behavior may occur at extremely long lengths.

Abstract

Numerical studies of some unidimensional systems suggest that Fourier law is satisfied, where theory predicts a divergence of heat conductivity with the system size. Here, I revisit some such models, finding that in all cases a divergence asymptotically emerges. This includes a variant of the ding-a-ling model, where I find that, contrary to previous claims, the ``anomalous" growth starts already for moderate system sizes. More conceptually interesting is the case of non-binding potentials, whose behavior is well reproduced by assuming that the energy flux across the nonequilibrium stationary state is the sum of two contributions: a diffusive and a hydrodynamic one. This approach, which extends an idea previously formulated for nearly integrable systems, allows to conclude that the asymptotic regime is always dominated by the anomalous hydrodynamic component, but the crossover may occur for extremely long system sizes.