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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Quantum laws and Aharonov-Bohm effect

P. Bocchieri, A. Loinger

Published Feb 1, 1984• 15 citations
Publisher
DOI
10.1007/bf02800258

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The Aharonov-Bohm effect is considered by most authors as a quantum effect, but a generally accepted explanation does not seem to be available. The phenomenon is studied here under the assumption that hypothetical electric dipole distributions configured by moving charges in the solenoid act on the electrons as test particles. The relative motions of the interacting charged particles introduce relativistic time dilations. The massless dipoles are postulated as part of an impact model that has recently been proposed to account for the far-reaching electrostatic forces between charged particles described by Coulomb's law. The model provides a quantitative explanation of the Aharonov-Bohm effect.

arXiv:1501.05261•Aug 23, 2014•1 citation
We investigate the role of Faraday's law of induction manifested in the quantum state of Aharonov-Bohm (AB) loops. In particular, a flux-switching experiment is proposed for a double-dot AB loop to verify the phase shift induced by Faraday's law. The induced Faraday phase is shown to be geometric and nontopological. This study demonstrates that the relation between the local phases of a ring at different fluxes is not arbitrary but is instead determined by Faraday's inductive law, which is in contrast to the arbitrary local phase of an AB loop for a given flux.
Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.
The Aharonov-Bohm effect is considered by most authors as a quantum effect, but a generally accepted explanation does not seem to be available. The phenomenon is studied here under the assumption that hypothetical electric dipole distributions configured by moving charges in the solenoid act on the electrons as test particles. The relative motions of the interacting charged particles introduce relativistic time dilations. The massless dipoles are postulated as part of an impact model that has recently been proposed to account for the far-reaching electrostatic forces between charged particles described by Coulomb's law. The model provides a quantitative explanation of the Aharonov-Bohm effect.