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Journal of Plasma Physics

Some surprising manifestations of charged particle dynamics in a magnetic field

Ram K. Varma

Published Jan 15, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1017/s0022377809990626

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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.
Abstract This review describes the results of investigations on charged particle dynamics in a magnetic field carried out over a number of years. The studies have unravelled the existence of some very surprising and unusual phenomena. Though existing on the macro-scale, they are found to be of quantum origin, and are thereby not covered by the Lorentz equation, which has been regarded conventionally as the descriptor of electrodynamic phenomena on the macro-scale. These novel phenomena have been found to be attributed to the ‘quantum modulation’ of the de Broglie wave along the magnetic field. This is brought about through the scattering-induced transition across Landau levels, leading to the modulation of the plane wave state along the field as a result of the entanglement between the parallel and perpendicular degrees of freedom. These findings were motivated by the predictions of a formalism developed by the author and include such unusual phenomena as (i) macro-scale matter wave interference effects and (ii) the detection of curl-free vector potential also on the macro-scale, both attributed to quantum modulation which is a matter wave on the macro-scale. The formalism is thus described as ‘macro-quantization of guiding centre motion’.
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.
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.
Matter wave interference effects in the macrodomain for charged particles in a magnetic field are reported for different scatterer positions between the electron gun and collector plate. The results obtained serve to validate and establish the important premises of the formalism that it is the scattering, ( inter alia off the grid wires in this case) which generates the transition amplitude waves resulting in the novel quantum effects observed on the macro-scale associated with the transition amplitude wave. The variation of the position of origin of the grid-generated transition amplitude wave then leads to the variation of interference characteristics accordingly in the plate and grid currents. A Fourier decomposition of the interference peaks reveal also the presence of harmonics which are a manifestation of the Landau level structure. A rich class of quantum phenomena are thus discovered in the simple dynamical system of charged particles in a magnetic field in the ostensibly classical domain of operation, with the transition amplitude wave generated as a consequence of scattering being the new element of quantum description on the macro-scale.
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 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.