  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.
