Dynamics of a classical Hall system driven by a time-dependent Aharonov--Bohm flux

TL;DR

This paper investigates the classical dynamics of a charged particle in a plane with a time-dependent Aharonov--Bohm flux, revealing a transition from localized spirals to conducting cycloid motion with diffusive drift.

Contribution

It introduces a detailed analysis of classical particle trajectories under a time-dependent flux, highlighting a novel localization-delocalization transition in the system.

Findings

Trajectories spiral inward and lose energy in the past.

Particles become conducting and drift orthogonally to the electric field after hitting the flux.

The system exhibits a localization to delocalization transition.

Abstract

We study the dynamics of a classical particle moving in a punctured plane under the influence of a strong homogeneous magnetic field, an electrical background, and driven by a time-dependent singular flux tube through the hole. We exhibit a striking classical (de)localization effect: in the far past the trajectories are spirals around a bound center; the particle moves inward towards the flux tube loosing kinetic energy. After hitting the puncture it becomes ``conducting'': the motion is a cycloid around a center whose drift is outgoing, orthogonal to the electric field, diffusive, and without energy loss.