Chaotic behaviour of disordered nonlinear lattices

TL;DR

This thesis investigates energy transport in disordered nonlinear lattice models, revealing persistent chaotic transport and dynamic hotspots, and introduces efficient numerical methods for studying these complex systems.

Contribution

It provides a detailed analysis of chaotic energy transport mechanisms in disordered nonlinear lattices and develops computationally efficient symplectic integrators for their simulation.

Findings

Chaotic transport persists in nonlinear disordered lattices.

Chaotic hotspots meander and support energy spreading.

Efficient symplectic integrators are implemented for these models.

Abstract

This thesis focuses on the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We report the effects of the type of the impurity (heterogeneity) parameter on the systems' transport properties and classifies the transport mechanisms of the nonlinear versions of the models into various dynamical regimes. We also identify computationally efficient numerical integration techniques, including the so-called symplectic integrators, and implement them for studying these models. Finally, we perform an extensive numerical investigation of the dynamics of the considered models revealing that for their nonlinear versions chaotic transport persists and chaotic hotspots meander in the region of energy concentration supporting the spreading mechanism.