A charged particle in a homogeneous magnetic field accelerated by a time periodic Aharonov-Bohm flux

TL;DR

This paper studies how a charged quantum particle accelerates in a magnetic field when subjected to a sinusoidally varying Aharonov-Bohm flux, showing linear energy growth at resonance.

Contribution

It introduces a model combining magnetic fields and time-dependent flux, deriving an explicit acceleration rate using quantum averaging, and validating it numerically.

Findings

Particle energy increases linearly over time at resonance.

Explicit formula for acceleration rate matches numerical results.

Resonance condition leads to sustained acceleration.

Abstract

We consider a nonrelativistic quantum charged particle moving on a plane under the influence of a uniform magnetic field and driven by a periodically time-dependent Aharonov-Bohm flux. We observe an acceleration effect in the case when the Aharonov-Bohm flux depends on time as a sinusoidal function whose frequency is in resonance with the cyclotron frequency. In particular, the energy of the particle increases linearly for large times. An explicit formula for the acceleration rate is derived with the aid of the quantum averaging method, and then it is checked against a numerical solution with a very good agreement.