Universality of one-dimensional heat conductivity

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.