On the anomalous thermal conductivity of one-dimensional lattices

TL;DR

This paper investigates why one-dimensional lattices exhibit anomalously divergent thermal conductivity, using numerical simulations, theoretical analysis, and mode-coupling theory to understand the underlying physical mechanisms.

Contribution

It provides a comprehensive analysis of the divergence law of thermal conductivity in 1D lattices using multiple approaches and links the anomaly to slow energy diffusion of long-wavelength modes.

Findings

Thermal conductivity diverges with system size in 1D lattices.

Energy diffusion of long-wavelength modes is anomalously slow.

Numerical results align with mode-coupling theory predictions.

Abstract

The divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated. The divergence law is consistently determined with two different numerical approaches based on equilibrium and non-equilibrium simulations. A possible explanation in the framework of linear-response theory is also presented, which traces back the physical origin of this anomaly to the slow diffusion of the energy of long-wavelength Fourier modes. Finally, the results of dynamical simulations are compared with the predictions of mode-coupling theory.