Billiards in magnetic fields: A molecular dynamics approach

TL;DR

This paper introduces a classical molecular dynamics computational scheme to analyze chaotic billiards in magnetic fields, capable of handling complex geometries and multiple particles, with applications in nanostructure transport systems.

Contribution

The paper presents a novel molecular dynamics approach for simulating billiards in magnetic fields, accommodating arbitrary geometries and multiple interacting particles.

Findings

Regularity islands at integer aspect ratios in single-particle billiards

Chaotic behavior dominates in two Coulomb-interacting particles

Quasiperiodic and regular trajectories observed under different conditions

Abstract

We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for rectangular single-particle billiards in magnetic fields and find a sequence of regularity islands at integer aspect ratios. In the case of two Coulomb-interacting particles the dynamics is dominated by chaotic behavior. However, signatures of quasiperiodicity can be identified at weak interactions, as well as regular trajectories at strong magnetic fields. Our scheme provides a promising tool to monitor the classical limit of many-electron semiconductor nanostructures and transport systems up to high magnetic fields.