Scaling properties of energy spreading in nonlinear Hamiltonian two-dimensional lattices

TL;DR

This study investigates energy spreading in two-dimensional nonlinear Hamiltonian lattices, demonstrating that the subdiffusive behavior aligns with nonlinear diffusion equation predictions and occurs even without disorder.

Contribution

It extends the universality class of subdiffusive energy spreading to two-dimensional lattices and shows that chaos-driven diffusion does not require disorder.

Findings

Scaling predictions from NDE match numerical results

Scaling also applies to regular nonlinear lattices

Analytical estimates of the scaling exponent are provided

Abstract

In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion equation (NDE) has been suggested and checked for one-dimensional lattices. Here, we apply this approach to two-dimensional strongly nonlinear lattices and find a nice agreement of the scaling predicted from the NDE with the spreading results from extensive numerical studies. Moreover, we show that the scaling works also for regular lattices with strongly nonlinear coupling, for which the scaling exponent is estimated analytically. This shows that the process of chaotic diffusion in such lattices does not require disorder.