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arXiv:0901.2618 · Physics Letters B

Induced fractional zero-point angular momentum for charged particles of the Bohm–Aharonov system by means of a “spectator” magnetic field

Jian-zu Zhang A B

Published Nov 8, 2008• 10 citations
arXivHTMLPDF

Abstract

An induced fractional zero-point angular momentum of charged particles by the Bohm–Aharonov (BA) vector potential is realized via a modified combined trap. It explores a “spectator” mechanism in this type of quantum effects: In the limit of the kinetic energy approaching one of its eigenvalues the BA vector potential alone cannot induce a fractional zero-point angular momentum at quantum mechanical level in the BA magnetic field-free region; But when there is a “spectator” magnetic field the BA vector potential induces a fractional zero-point angular momentum. The “spectator” does not contribute to such a fractional angular momentum, but plays essential role in guaranteeing non-trivial dynamics at quantum mechanical level in the required limit. This “spectator” mechanism is significant in investigating the BA effects and related topics in both aspects of theory and experiment.

DOI
10.1016/j.physletb.2008.10.056

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An induced fractional zero-point angular momentum of charged particles by the Bohm–Aharonov (BA) vector potential is realized via a modified combined trap. It explores a “spectator” mechanism in this type of quantum effects: In the limit of the kinetic energy approaching one of its eigenvalues the BA vector potential alone cannot induce a fractional zero-point angular momentum at quantum mechanical level in the BA magnetic field-free region; But when there is a “spectator” magnetic field the BA vector potential induces a fractional zero-point angular momentum. The “spectator” does not contribute to such a fractional angular momentum, but plays essential role in guaranteeing non-trivial dynamics at quantum mechanical level in the required limit. This “spectator” mechanism is significant in investigating the BA effects and related topics in both aspects of theory and experiment.
The induced fractional zero-point canonical angular momentum on charged particles by the Aharonov - Bohm (AB) vector potential is realized via modified combined traps. It explores new features for this type of quantum effects: In a limit of vanishing mechanical kinetic energy the AB vector potential alone cannot induce a fractional zero-point canonical angular momentum on charged particles at the quantum mechanical level in the AB magnetic field-free region; But for the case of the AB vector potential with another one of a "spectator" magnetic field the AB vector potential induces a fractional zero-point canonical angular momentum in the same limit. The "spectator" one does not contribute to such a fractional zero-point quantity, but plays essential role in guaranteeing non-trivial dynamics survived in this limit at the quantum mechanical level. These results are significance in investigations of the AB effects and related fields for both theories and experiments.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux  through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc     , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.
In the context of the Aharonov-Bohm effect, it is well-known that the local action of the vector potential or the non-local action of the magnetic field are properties attributable to quantum physics, which can explain the observed Aharonov-Bohm phase. Here we point out that, surprisingly, these properties are also attributable to classical physics and that this result follows from examining the electromagnetic angular momentum of a static electric charge outside an infinitely-long solenoid of finite radius carrying a uniform magnetic flux. This angular momentum may be expressed in three equivalent forms. The first form shows that there is an electromagnetic angular momentum even in regions for which the magnetic field vanishes but the potential does not, which stresses the physical nature of the vector potential in classical physics. The second form shows that there is an electromagnetic angular momentum produced by the non-local action of the magnetic field. The third form shows that the Aharonov-Bohm phase is proportional to the magnitude of the electromagnetic angular momentum, which sheds light on the physical meaning of this phase.
Abstract The charged particle confined by a harmonic potential in a noncommutative planar phase space interacting with a homogeneous dynamical magnetic field and Aharonov-Bohm potentials is studied. We find that the canonical orbital angular momenta of the reduced models, which are obtained by setting the mass and a dimensionless parameter to zero, take fractional values. These fractional angular momenta are not only determined by the flux inside the thin long solenoid but also affected by the noncommutativities of phase space.
An experiment to observe the Aharonov-Bohm effect is discussed. A solenoid which consists of a large number of point magnetic dipoles is considered as the source of a vector potential, which acts on a charged particle, and such potential has an electromagnetic field of zero strength in the region of a nonzero vector potential. A detailed microscopic analysis of the change in the quantum state phase of the entire system, namely, a particle and a set of dipoles, reveals the origin of the apparent nonlocality of the action of the vector potential, and shows the locality of the phase change mechanism. An analysis of an experiment with a solenoid shielded by a superconducting shell is given.