Two interacting particles in the Harper model

TL;DR

This paper investigates how interactions between two particles affect their localization and spectral properties in the Harper model, revealing that interactions can induce localization and spectral changes.

Contribution

It demonstrates that particle interactions induce localization and spectral modifications in the Harper model, contrasting with behavior in random potentials.

Findings

Interaction induces localized states in the Harper model.

Interaction leads to pure-point spectrum in certain regimes.

In the localized phase, interaction enhances localization.

Abstract

Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case when noninteractive system is quasi-diffusive or ballistic. In the localized phase interaction gives only stronger localization contrary to the case of two interacting particles in a random potential.