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arXiv:quant-ph/0201133

New type of fields in Maxwells equations: their properties and method of detection

A. G. Chirkov, A. N. Ageev

Published Jan 29, 2002• 0 citations
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Abstract

A theoretical analysis of the excitation of an infinitely long solenoid by oscillating current has revealed the existence of specific potentials in the space outside the solenoid, which can affect electron diffraction in an experiment similar to the Aharonov-Bohm effect. Thus, these time-dependent potentials are physical fields possessing a number of specific features, which set them off from the fields known heretofore.

DOI
10.48550/arxiv.quant-ph/0201133

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A theoretical analysis of the excitation of an infinitely long solenoid by oscillating current has revealed the existence of specific potentials in the space outside the solenoid, which can affect electron diffraction in an experiment similar to the Aharonov-Bohm effect. Thus, these time-dependent potentials are physical fields possessing a number of specific features, which set them off from the fields known heretofore.
Whether the time-dependent Aharonov-Bohm (AB) effect even exists or not has been the subject of long-standing debate. There are two factors complicating the problem. First, in the closed spacetime line integral of the vector potential that is thought to give the AB-phase shift, how to treat the time-varying vector potential is highly nontrivial. Second, the time-varying magnetic flux generates induced electric field even outside the solenoid. In the present paper, motivated by a recent work by Gao, we re-investigate the role of the induced electric field with the utmost care. This analysis reveals a highly nontrivial effect of the induced electric field, which turns out to be useful for verifying the very existence of the time-dependent AB-effect.
"It is a known fact that there is no magnetic field outside an infinite solenoid carrying a constant current, althoughthere is magnetic vector potential non-null outside it. The existence of the Aharonov-Bohm effect (AB) is usuallyconsidered as proof of the relevance of the vector potential for quantum mechanics. In this paper we will see that thereis a non null electric field outside an infinite resistive solenoid carrying a constant current and its possible relevanceto the analysis of the Aharonov-Bohm effect. When calculating, we introduce the Galilean invariance of Maxwell´sequations and then we obtain the contribution to the AB effect due to electric potential."
The case where the magnetic flux inside an electronic loop varies with time is considered for an experiment in which the Aharonov-Bohm effect is observed. The electromagnetic field and potentials of a solenoid with an alternating current are studied. It is shown that the vector potential outside the solenoid contains a term corresponding to a zero electromagnetic field at the same point of space. This part of the potential (global potential) describes standing waves whose properties differ from those of ordinary electromagnetic waves and which can be conventionally called information potential waves. A method of detecting information waves is proposed involving an effect similar to the Aharonov-Bohm effect (quasi-Aharonov-Bohm effect). Unlike ordinary electromagnetic waves, these information waves are not involved in any energy interactions but they can carry information.
We discuss two possible covariant generalizations of the Aharonov–Bohm effect – one expression in terms of the space–time line integral of the four-vector potential and the other expression in terms of the space–time “area” integral of the electric and magnetic fields written in terms of the Faraday 2-form. These expressions allow one to calculate the Aharonov–Bohm effect for time-dependent situations. In particular, we use these expressions to study the case of an infinite solenoid with a time varying flux and find that the phase shift is zero due to a cancellation of the Aharonov–Bohm phase shift with a phase shift coming from the Lorentz force associated with the electric field, E=−∂tA, outside the solenoid. This result may already have been confirmed experimentally.