Power-law divergent heat conductivity in one-dimensional momentum-conserving nonlinear lattices

We numerically study heat conduction in a few one-dimensional Fermi-Pasta-Ulam (FPU)-type lattices by both nonequilibrium heat bath and equilibrium Green-Kubo algorithms. In those lattices, heat conductivity κ is known to diverge with length N as N α . It is commonly expected that the running exponent α should monotonously decreases with N and a recent study has shown that α for the FPU-β lattice saturates to 1/3 as N ∼10 4 . However, our calculations clearly show that α changes its behaviour, increasing towards the asymptotic value 2/5 for yet larger N values. As for the purely quartic lattice, α=2/5 is clearly observed in four orders of magnitude of N ranging from 10 2 to 10 6 . This unexpected reversal phenomenon can be observed more clearly in a much shorter FPU-αβ lattice.