Heat conduction in 2d nonlinear lattices

TL;DR

This study investigates heat conduction in 2D anharmonic lattices, revealing a logarithmic divergence of conductivity in chaotic regimes and superanomalous transport in less chaotic regimes, supported by numerical and analytical methods.

Contribution

It provides the first comprehensive analysis combining numerical simulations and theoretical estimates to understand heat transport anomalies in 2D nonlinear lattices.

Findings

Logarithmic divergence of heat conductivity in ergodic regimes.

Confirmation of anomalous transport via linear-response theory.

Evidence of superanomalous transport in weakly chaotic regimes.

Abstract

The divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials. Two different numerical approaches based on nonequilibrium and equilibrium simulations provide consistent indications in favour of a logarithmic divergence in "ergodic", i.e. highly chaotic, dynamical regimes. Analytical estimates obtained in the framework of linear-response theory confirm this finding, while tracing back the physical origin of this {\sl anomalous} transport to the slow diffusion of the energy of long-wavelength effective Fourier modes. Finally, numerical evidence of {\sl superanomalous} transport is given in the weakly chaotic regime, typically found below some energy density threshold.