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Physica Scripta

Observation of the Magnetic Vector Potential à la Aharonov-Bohm Along One Dimension in a Magnetic Field in the Correspondence Limit

Ram K. Varma

Published Jan 1, 2005• 1 citation
Publisher

Abstract

We report here the observation of the curl-free vector potential a la' Aharonov-Bohm in the classical macro-domain for one-dimensional motion of a charged particle in a magnetic field. The nature of this observation is emphasized here as being a hitherto unfamiliar quantum manifestation of the behaviour of the transition amplitude in the correspondence limit of large Landau quantum numbers.

DOI
10.1238/physica.topical.116a00038

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Journal of Plasma Physics•Jan 15, 2010•2 citations
We report here the observation of the curl-free vector potential a la' Aharonov-Bohm in the classical macro-domain for one-dimensional motion of a charged particle in a magnetic field. The nature of this observation is emphasized here as being a hitherto unfamiliar quantum manifestation of the behaviour of the transition amplitude in the correspondence limit of large Landau quantum numbers.
The recently reported curl-free vector potential observation (Varma et al 2012 Eur. Phys. J. D 66 38) in relation to a system of charged particles in a magnetic field points to the existence of a new state of the electron—a quantum modulated state—which arises through a scattering-induced transition across Landau levels. This quantum modulated state has been shown to account for some very unusual effects on the macro-scale, which are distinct from the ones which can be understood in terms of a 'classical electron' and also from the ones which can be understood in terms of a 'quantum electron' on the micro-scale characterized by the Planck quantum. This quantum modulated state has been shown to account for the observation of a static curl-free vector potential on the macro-scale alluded to above, as well as other matter wave manifestations on the macro-scale. The macro-scale curl-free vector potential observation differs fundamentally from the corresponding micro-scale effect—the well-known Aharonov–Bohm effect. These two effects—on the macro-scale and the macro-scale—are compared and contrasted to each other here in their manner of detection of the static curl-free vector potential. Such a comparative study helps gain a deeper understanding of the nature of the quantum modulated state and the macro-scale matter wave it represents.
The recently reported curl-free vector potential observation on the macro-scale, which has been attributed to a macro-scale matter wave associated with the quantum modulation of the de Broglie wave along the magnetic field, is seen to be in apparent contravention with the Lorentz equation of classical electrodynamics, which as a descriptor on the macro-scale takes no cognizance of a curl-free vector potential. The two different formalisms?a deterministic one ? la Lorentz and a probabilistic one by the quantum modulation?both existing on the macro-scale and, though in apparent contravention, complement each other and are essential for a complete description of all phenomena relating to charged particle dynamics. The quantum modulations which arise in consequence of transition across Landau levels appear as ?hole? auto-excitations in the Lorentz trajectory involving internal inelastic scattering. This lends a new dimension to the Lorentz trajectory which, though on the classical macro-scale, acts like a ?quantum resonator? and can now exist in a number of self-excited states labelled by the Landau level interval involved in the excitation, and which are of quantum origin and on the macro-scale, with the quantum modulations being the excitations.
Abstract We point the rather unusual existence of a potential embedding in the Lorentz trajectory – charged particle trajectory in a magnetic field – of a one-dimensional matter wave dynamics on the macro-scale as demonstrated through one-dimensional matter wave interference effects on the macro-scale, as well as the observation of a curl-free vector potential in one dimension, also on the macro-scale. Such an embedding is a manifestation of the generation of the quantum modulation of the de Broglie wave of the particle along the magnetic field, arising concomitantly, with a scattering-induced transition across Landau levels in consequence of quantum entanglement between the parallel and perpendicular degrees of freedom.
I present conclusive arguments to show that a recent claim of observation of quantum-like effects of the magnetic vector potential in the classical macrodomain is spurious. The `one dimensional interference patterns' referred to in the paper by R. K. Varma et al (Phys. Lett. A 303 (2002) 114-120) are not due to any quantum-like wave phenomena. The data reported in the paper are not consistent with the interpretation of interference, or with the topology of the Aharonov-Bohm effect. The assertion that they are evidence of A-B like effect in the classical macrodomain is based on inadequate appreciation of basic physical facts regarding classical motion of electrons in magnetic fields, interference phenomena, and the A-B effect.
The set of Schrödinger-like equations obtained earlier by the author [Phys. Rev. Lett. 26, 417 (1971), Phys. Rev. A 31, 3951 (1985)] for the charged particle dynamics in an inhomogeneous magnetic field in the macrodomain, are derived here starting from the quantum-mechanic Schrödinger equation in its path-integral representation. This derivation enables a generalization of the equations to include a curl-free vector potential in the Schrödinger-like equations. In view of the amplitude character of the latter equations, which now descends directly from that of the quantum-mechanic Schrödinger equation, they now predict the existence in the macrodomain of all such phenomena, which are characteristic of a probability amplitude theory, e.g., the interference, and the observation of a curl-free vector à la Aharonov-Bohm. A discrete energy structure, predicted as interference maxima and minima has already been observed by the author with his co-workers [Mod. Phys. Lett. A 8, 167 (1993)]. A prediction is now made for the observability of a curl-free vector potential in the macrodomain, in the context of the present problem.
Abstract We present here some very unusual experimental results on the dynamics of charged particle in a magnetic field which cannot be comprehended in terms of the Lorentz dynamics regarded, as per the current conceptual framework, as the appropriate one for the macro-scale description. Astonishingly, these results have been shown to be manifestations of a novel macro-scale quantum structure, designated as ‘transition amplitude wave’ (TAW), riding with the guiding centre trajectory, which is generated in the latter trajectory in consequence of the scattering of the particle with a fixed scattering centre. One set of observed results is thus identified as matter wave interference effects on the macro-scale attributable to this entity. The other enigmatic observation demonstrates the detection of a curl-free magnetic vector potential on the macro-scale, which is also shown to be a consequence of the TAW embedded in the Lorentz trajectory. These enigmatic results thus point to the unravelling of a new concept of a ‘dressed’ Lorentz trajectory—dressed with the TAW—accountable for these results, as against the ‘bare’ trajectory. These results and the formalism which enables one to comprehend them have led to the emergence of a new class of phenomena which display quantum properties on the macro-scale.