Chaotic properties of Coulomb-interacting circular billiards

TL;DR

This study investigates the chaotic dynamics of a two-electron circular billiard system with Coulomb interactions, revealing how interaction strength influences orbit behavior and phase space chaos, with implications for quantum dot models.

Contribution

The paper provides an analytic expression for bouncing maps in strongly interacting regimes and compares it with numerical data, advancing understanding of classical chaos in Coulomb-interacting systems.

Findings

Weak interactions cause jumps between quasi-regular orbits.

Strong interactions allow an analytic bouncing map expression.

Escape rates are exponential, indicating strong chaos.

Abstract

We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more quantitative view on the dynamics as the interaction strength is varied, we compute and analyze the escape rates of the system. Apart from very weak or strong interactions, the escape rates show consistently exponential behavior, thus suggesting strongly chaotic dynamics and a phase space without significant sticky regions within the considered time scales.