Universality of One-Dimensional Heat Conductivity

Abstract

We show analytically that the heat conductivity of oscillator chains diverges with system size N as N^{1/3}, which is the same as for one-dimensional fluids. For long cylinders, we use the hydrodynamic equations for a crystal in one dimension. This is appropriate for stiff systems such as nanotubes, where the eventual crossover to a fluid only sets in at unrealistically large N. Despite the extra equation compared to a fluid, the scaling of the heat conductivity is unchanged. For strictly one-dimensional chains, we show that the dynamic equations are those of a fluid at all length scales even if the static order extends to very large N. The discrepancy between our results and numerical simulations on Fermi-Pasta-Ulam chains is discussed.

arXiv comment7 pages, 2 figures

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• Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential
• Heat conduction and diffusion of hard disks in a narrow channel
• Thermal expansion in nanoresonators