Spreading of energy in the Ding-Dong Model

TL;DR

This paper investigates how energy propagates in a lattice of colliding harmonic oscillators, revealing different spreading mechanisms in regular versus disordered configurations, with implications for understanding energy localization.

Contribution

It introduces the Ding-Dong model to analyze energy spreading, highlighting the roles of compactons and chaotic breathers in regular lattices and the cessation of spreading in disordered ones.

Findings

Energy spreading is mediated by compactons and breathers in regular lattices.

Disorder prevents compacton formation, halting energy spread.

Disordered lattices stabilize into finite configurations with chaotic spots.

Abstract

We study properties of energy spreading in a lattice of elastically colliding harmonic oscillators (Ding-Dong model). We demonstrate that in the regular lattice the spreading from a localized initial state is mediated by compactons and chaotic breathers. In a disordered lattice the compactons do not exist, and the spreading eventually stops, resulting in a finite configuration with a few chaotic spots.