# Anomalous energy diffusion in two-dimensional nonlinear lattices

## TL;DR

This study uses fluctuation correlation functions to demonstrate that energy diffusion in two-dimensional nonlinear lattices is anomalous, characterized by Levy-stable distributions, and explores the effects of harmonic interactions and nonlinear potentials on heat transport.

## Contribution

It provides the first detailed simulation evidence that energy diffusion in 2D momentum-conserving lattices is anomalous, challenging previous assumptions based on 1D systems.

## Key findings

- Energy diffusion in 2D lattices is anomalous and Levy-stable.
- Disappearance of heat mode side peaks suggests weak coupling with sound mode.
- Harmonic interactions accelerate energy diffusion in 2D lattices.

## Abstract

Heat transport in one-dimensional (1D) momentum-conserving lattices is generally assumed to be anomalous, thus yielding a power-law divergence of thermal conductivity with system length. However, whether heat transport in two-dimensional (2D) system is anomalous or not is still on debate because of the difficulties involved in experimental measurements or due to the insufficiently large simulation size. Here, we simulate energy and momentum diffusion in the 2D nonlinear lattices using the method of fluctuation correlation functions. Our simulations confirm that energy diffusion in the 2D momentum-conserving lattices is anomalous and can be well described by the L\'{e}vy-stable distribution. We also find that the disappear of side peaks of heat mode may suggest a weak coupling between heat mode and sound mode in the 2D nonlinear system. It is also observed that the harmonic interactions in the 2D nonlinear lattices can accelerate the energy diffusion. Contrary to the hypothesis of 1D system, we clarify that anomalous heat transport in the 2D momentum-conserving system cannot be corroborated by the momentum superdiffusion any more. Moreover, as is expected, lattices with a nonlinear on-site potential exhibit normal energy diffusion, independent of the dimension. Our findings offer some valuable insights into the mechanism of thermal transport in 2D system.