Scaling of energy spreading in a disordered Ding-Dong lattice

TL;DR

This study investigates energy propagation in a disordered Ding-Ding lattice, revealing irregular, subdiffusive spreading influenced by chaos, with spreading exponents weakly affected by different types of disorder.

Contribution

It demonstrates that energy spreading in a disordered Ding-Ding lattice follows a scaling law and is weakly dependent on disorder type, advancing understanding of wave dynamics in nonlinear disordered systems.

Findings

Energy spreading is irregular and subdiffusive.

Spreading exponents are weakly affected by disorder type.

Mean waiting times follow a scaling law with energy.

Abstract

We study numerically propagation of energy in a one dimensional Ding-Ding lattice, composed of linear oscillators with ellastic collisions. Wave propagation is suppressed by breaking translational symmetry, we consider three way to do this: a position disorder, a mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an initially localized wavepacket is irregular, due to appearance of chaos, and subdiffusive. Guided by a nonlinear diffusion equation, we establish that the mean waiting times of spreading obey a scaling law in dependence on energy. Moreover, we show that the spreading exponents very weakly depend on the level of disorder.