Energy Spreading in Strongly Nonlinear Disordered Lattices

TL;DR

This paper investigates how energy spreads in strongly nonlinear disordered lattices, revealing subdiffusive behavior and validating a fractional nonlinear diffusion model to describe the scaling properties of this process.

Contribution

It introduces a fractional nonlinear diffusion equation as a heuristic model for energy spreading in strongly nonlinear disordered lattices and confirms its applicability across various cases.

Findings

Energy spreading is subdiffusive and slower than power law in linear oscillators.

Power law spreading is observed in nonlinear local oscillators.

Scaling predictions from the fractional nonlinear diffusion model match numerical results.

Abstract

We study scaling properties of energy spreading in disordered strongly nonlinear Hamiltonian lattices. Such lattices consist of nonlinearly coupled local linear or nonlinear oscillators, and demonstrate a rather slow, subdiffusive spreading of initially localized wave p ackets. We use a fractional nonlinear diffusion equation as a heuristic model of this process, and confirm that the scaling predictions resulting from a self-similar solution of this equation are indeed applicable to all studied cases. We s how that the spreading in nonlinearly coupled linear oscillators slows down compared to a pure power law, while for nonlinear local oscillators a power law is valid in the whole studied range of parameters.