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Journal of Physics A Mathematical and General

How does quantum impenetrability affect Aharonov-Bohm scattering?

G N Afanasiev, V.M. Shilov

Published Nov 21, 1990• 6 citations
Publisher

Abstract

It is shown that different forms of quantum impenetrability lead to different physical consequences. This should be kept in mind in analysing experimental data. The relativistic impenetrability conditions are considered and the corresponding relativistic Aharonov-Bohm cross-sections are obtained. The possibility of the AB effect occurring in simply-connected space regions is discussed.

DOI
10.1088/0305-4470/23/22/012

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It is shown that different forms of quantum impenetrability lead to different physical consequences. This should be kept in mind in analysing experimental data. The relativistic impenetrability conditions are considered and the corresponding relativistic Aharonov-Bohm cross-sections are obtained. The possibility of the AB effect occurring in simply-connected space regions is discussed.
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.
We study a generalization of Aharonov-Bohm effect, the potential effect. The discussion is focused on field-free effects in simply connected region, which obviously can not have any local field-flux. Among the published discussions about this kind of effects, it is generally agreed that this kind of effects does not exist due to gauge invariance. However, there are also opinions that this effect is a trivial variation of Aharonov-Bohm effect and therefore there is no need to check its existence. To my knowledge, it has never been tested. My first goal here is to supply enough theoretical reason to motivate the experimental test of this effect. I start with an intuitive derivation, then I introduce a wave-front theory as a theoretical consideration. Logically, the existence of potential effect implies the existence of the AB effect, but not vice versa. The purpose of this paper is to provide a physical connection in the opposite direction.
It is shown that electromagnetic effects of a vector potential on a charged particle confined to a region RRR (multiply or simply connected) are completely determined by field strengths in RRR, if the potential obeys certain conditions. Such potentials are adequate in experiments purporting to show Aharonov-Bohm effect. Therefore these experiments have not established effects of inaccessible fields.