# Heat current fluctuations and anomalous transport in low dimensional carbon lattices

## TL;DR

This study uses molecular dynamics to reveal that heat transport in low-dimensional carbon structures like nanotubes and graphene is anomalous, with size-dependent thermal conductivity and nonlinear temperature profiles, indicating Levy walk behavior.

## Contribution

It demonstrates that heat conduction in carbon nanotubes and graphene deviates from Fourier's law, showing specific size-dependent scaling laws and universality class characteristics.

## Key findings

- Thermal conductivity in nanotubes scales as the square root of length.
- Thermal conductivity in graphene scales logarithmically with length.
- Heat transport is better described by Levy walk dynamics.

## Abstract

Molecular dynamics simulations and nonequilibrium importance sampling are used to study the heat transport of low dimensional carbon lattices. For both carbon nanotubes and graphene sheets heat transport is found to be anomalous, violating Fourier's law of conduction with a system size dependent thermal conductivity and concomitant nonlinear temperature profiles. For carbon nanotubes, the thermal conductivity is found to increase as the square root of the length of the nanotube, while for graphene sheets the thermal conductivity is found to increase as the logarithm of the length of the sheet. The particular length dependence and nonlinear temperature profiles place carbon lattices into a universality class with nonlinear lattice models, and suggest that heat transport through carbon nano-structures is better described by a Levy walk rather than simple diffusion.