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

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.

References in corpus (7)

• The Non-Commutative Geometry of the Quantum Hall Effect
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• Fractal Weyl Law for Open Chaotic Maps
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• Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux
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Cited by in corpus (2)

• On the dynamics created by a time--dependent Aharonov-Bohm flux
• A charged particle in a homogeneous magnetic field accelerated by a time periodic Aharonov-Bohm flux