Chaotic delocalization of two interacting particles in the classical Harper model

TL;DR

This paper investigates how interactions induce chaos and delocalization of two particles in the classical Harper model, revealing the formation of bound chaotic states called chaons that spread over the lattice.

Contribution

It demonstrates that interactions break integrability, leading to chaotic delocalization and the emergence of chaons, a new type of composite quasi-particle in the classical Harper model.

Findings

Chaotic propulsion causes diffusive spreading of particles.

Bound states called chaons form and remain localized.

Chaotic delocalization occurs for various interaction types.

Abstract

We study the problem of two interacting particles in the classical Harper model in the regime when one-particle motion is absolutely bounded inside one cell of periodic potential. The interaction between particles breaks integrability of classical motion leading to emergence of Hamiltonian dynamical chaos. At moderate interactions and certain energies above the mobility edge this chaos leads to a chaotic propulsion of two particles with their diffusive spreading over the whole space both in one and two dimensions. At the same time the distance between particles remains bounded by one or two periodic cells demonstrating appearance of new composite quasi-particles called chaons. The effect of chaotic delocalization of chaons is shown to be rather general being present for Coulomb and short range interactions. It is argued that such delocalized chaons can be observed in experiments with cold atoms and ions in optical lattices.