Energy diffusion in two-dimensional momentum-conserving nonlinear lattices: Levy walk and renormalized phonon

The energy diffusion process in a few two-dimensional Fermi-Pasta-Ulam-type lattices is numerically simu-lated via the equilibrium local energy spatiotemporal correlation. Just as the nonlinear fluctuating hydrodynamic theory suggested, the diffusion propagator consists of a bell-shaped central heat mode and a sound mode extending with a constant speed. The profiles of the heat and sound modes satisfy the scaling properties from a random-walk-with-velocity-fluctuation process very well. An effective phonon approach is proposed, which expects the frequencies of renormalized phonons as well as the sound speed with quite good accuracy. Since many existing analytical and numerical studies indicate that heat conduction in such two-dimensional momentum-conserving lattices is divergent and the thermal conductivity kappa increases logarithmically with lattice length, it is expected that the mean-square displacement of energy diffusion grows as t ln t. Discrepancies, however, are noticeably observed.

Automated summary

The energy diffusion process in a few two-dimensional Fermi-Pasta-Ulam-type lattices is simulated numerically through the equilibrium local energy spatiotemporal correlation. The diffusion propagator consists of a bell-shaped central heat mode and a sound mode extending with a constant speed, in accordance with the nonlinear fluctuating hydrodynamic theory. An effective phonon approach is proposed to estimate the frequencies of renormalized phonons and the sound speed accurately. However, discrepancies are noticeably observed.