Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

Details Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

2004-10-14

arxiv.org/abs/cond-mat/0410355v1

Physics

Condensed Matter

Statistical Mechanics

15 Revtex pages, 16 figures. Invited article for CHAOS focus issue commemorating the 50th anniversary of the Fermi-Pasta-Ulam

Scientific paper

10.1063/1.1832791

We study anomalous heat conduction and anomalous diffusion in low dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is $\sigma^2(t)\equiv <\Delta x^2> =2Dt^{\alpha} (0<\alpha\le 2)$, then the thermal conductivity can be expressed in terms of the system size $L$ as $\kappa = cL^{\beta}$ with $\beta=2-2/\alpha$. This result predicts that a normal diffusion ($\alpha =1$) implies a normal heat conduction obeying the Fourier law ($\beta=0$), a superdiffusion ($\alpha>1$) implies an anomalous heat conduction with a divergent thermal conductivity ($\beta>0$), and more interestingly, a subdiffusion ($\alpha <1$) implies an anomalous heat conduction with a convergent thermal conductivity ($\beta<0$), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.

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