The Aharonov-Bohm effect: Why it cannot be eliminated from quantum mechanics

The Aharonov-Bohm effect is a necessary and easily understood feature of conventional quantum mechanics. Attempts to remove it from the theory must involve a drastic change in our understanding of the quantization and conservation of angular momentum, or of the role of the classical equations of motion in quantum mechanics. The key point is that a charged particle is the source of an electric field which will penetrate a magnetic field from which the particle is excluded. The crossed fields contain angular momentum whose existence alters the motion of the particle because the total angular momentum is quantized.     

Finite correction to Aharonov-Bohm scattering by a contact potential

We study the influence of a contact (or delta) potential on the Aharonov-Bohm scattering of nonrelativistic particles. In general the contact potential has no effect on the scattering as expected. However, when the magnetic flux and the strength of the contact potential take some special values, the Aharonov-Bohm scattering cross-section is manifestly changed. It is shown that these special values correspond to the simultaneous existence of two half-bound states in two adjacent angular momentum channels. Two limiting processes are presented to deal with the singularity of the contact potential and results of the same nature are obtained.     

Nonconservation of angular momentum in aharonov-bohm scattering

Aharonov-Bohm (AB) scattering by the vector potential of an infinitely long impenetrable solenoid of zero radius which carries magnetic flux is shown to violate the conservation of angular momentum. The difficulty is due to improper boundary conditions for a scattering problem used by AB.     

Magnetic Manipulation of Massless Dirac Fermions in Graphene Quantum Dot

We have theoretically analyzed the quasibound states in a graphene quantum dot (GQD) with a magnetic flux Φ in the centre. It is shown that the two-fold time reversal degeneracy is broken and the quasibound states of GQD with positive/negative angular momentum shifted upwards /downwards with increasing the magnetic flux. The variation of the quasibound energy depends linearly on the magnetic flux, which is quite different from theparabolic relationship for Schrödinger electrons. The GQD's quasibound states spectrum shows an obvious Aharonov-Bohm (AB) oscillations with the magnetic flux. It is also shown that the quasibound state with energy equal to the barrier height becomes a bound state completely confined in GQD.     

On the Aharonov-Bohm effect for bound states

The following model is discussed: A charged particle is bound by some potential to the origin of a coordinate system in three-dimensional space, while a shielded magnetic flux threads an axis through the origin, thus producing an Aharonov-Bohm effect. The Hamiltonian, boundary conditions, wave functions, and energy levels for this model are derived, and in particular the properties of the operators of kinetic angular momentum are discussed. The results obtained shed new light on some more general questions pertaining to boundary conditions and to the theory of angular momentum.     

Probing Dual Asymmetric Transverse Spin Angular Momentum in Tightly Focused Vector Beams in Optical Tweezers

The spin-orbit interaction (SOI) of light generated by tight focusing in optical tweezers is regularly employed in generating angular momentum - both spin and orbital - the effects being extensively observed in trapped mesoscopic particles. Specifically, the transverse spin angular momentum (TSAM), which arises due to the longitudinal component of the electromagnetic field generated by tight focusing is of special interest, both in terms of fundamental studies and associated applications. This study provides an effective and optimal strategy for generating TSAM in optical tweezers by tightly focusing first-order radially and azimuthally polarized vector beams with no intrinsic angular momentum (AM) into a refractive index stratified medium. The choice of such input fields ensures that the longitudinal spin angular momentum (LSAM) arising from the electric (magnetic) field for the radial (azimuthal) polarization is zero. As a result, the effects of the electric and magnetic TSAM are exclusively observed separately in the case of input first-order radially and azimuthally polarized vector beams on single optically trapped birefringent particles. This research opens up new and simple avenues for exotic and complex particle manipulation in optical tweezers.     

Aharonov-Bohm signature for neutral polarized excitons in type-II quantum dot ensembles

The Aharonov-Bohm effect is commonly believed to be a typical feature of the motion of a charged particle interacting with the electromagnetic vector potential. Here we present a magnetophotoluminescence study of type-II InP/GaAs self-assembled quantum dots, revealing the Aharonov-Bohm-type oscillations for neutral excitons when the hole ground state changes its angular momentum from l(h)=0 to l(h)=1, 2, and 3. The hole-ring parameters derived from a simple model are in excellent agreement with the structural parameters for this system.     

Aharonov-Bohm shift as a shift in normal coordinates

The Aharonov-Bohm shift in a closed system is considered. The solenoid is a charged, rotating cylinder which is electrically neutral. This model of Henneberger and Opatrny has a Hamiltonian which is a quadratic form. This quadratic form is transformed to normal coordinates, so that the stationary states become self-evident. It is shown that, in the original system, it is the kinetic angular momentum which is quantized. Solutions of the problem for an electron inside the solenoid are discussed. It is shown that the rotating cylinder exhibits different behavior if the electron is in the magnetic field or if it is in the external region. An external field approximation which replaces the cylinder by a constant magnetic field therefore cannot yield a correct solution of the Schrödinger equation which is continuous at the surface of the solenoid.     

Electromagnetic angular momentum flux tensor in a medium

Electromagnetic angular momentum describes the ability of electromagnetic field to impose torque on matter. We show that for an electromagnetic field ?C such as an optical beam field ?C in a medium, the torque density is determined by two fundamental quantities: the angular momentum flux tensor and the angular momentum density of the field. It is remarkable that the tensor alone gives the full picture of the angular momentum transfer between the field and the medium in all stationary electromagnetic phenomena. We derive a general expression for this tensor and apply the theory to several important examples without resorting to the classical paraxial approximation.     

Beams of electromagnetic radiation carrying angular momentum: The Riemann-Silberstein vector and the classical-quantum correspondence

All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann-Silberstein vector - a complex combination of the electric and magnetic field vectors - that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre-Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.     

Electromagnetic momentum, magnetic model of light and effects of the Aharonov-Bohm type

The wave equation for light propagation in slowly moving media, which is analogous to that of quantum effects of the Aharonov-Bohm type, is characterized by the interaction momentum , related to the flow . In effects of the Aharonov-Bohm type the interaction momentum is related to the momentum of the electromagnetic (em) fields, that characterizes an em flow . It is shown that in both cases has the same physical origin. Calculation of the interaction em momentum for the light wave dragged by the flow yields exactly the Fresnel-Fizeau momentum. These results corroborate the validity of the magnetic model for light and highlight the role and relevance of the em momentum in new effects of classical and quantum physics. A tentative test of an astrophysical Fizeau-Aharonov-Bohm effect is discussed.     

Electromagnetic momentum in frontiers of modern physics

We review the role of the momentum of the electromagnetic (EM) fields P_e in several areas of modern physics. P_e represents the EM interaction in equations for matter and t waves propagation. As an application of wave propagation properties, a first order optical experiment which tests the speed of light in moving rarefied gases is presented. Within a classical context, the momentum P_e appears also in proposed tests of EM interactions involving open currents and angular momentum conservation laws.Moreover, P_e is the link to the unitary vision of the quantum effects of the Aharonov-Bohm (AB) type and, for several of these effects, the strength of P_e is evaluated. These effects provide a quantum approach to evaluate the limit of the photon mass m_ph. A new effect of the AB type, together with the scalar AB effect, provides the basis for table-top experiments which yield the limit m_ph = 9.4 × 10^-52 g, a value that improves the results achieved with recent classical and quantum approaches.     

Dirac Particle in an Aharonov-Bohm Potential: The Structure of the First Order S-matrix

The structure of the interaction Hamiltonian in the first order S-matrix element of a Dirac particle in an Aharonov-Bohm (AB) field is analyzed and shown to have interesting interesting algebraic properties. It is demonstrated that as a consequence of these properties, this interaction Hamiltonian splits both the incident and outgoing waves in the the first order components (eigenstates of the third component of the spin). The matrix element can then be viewed as the sum of two transitions taking place in these two channels of the spin. At the level of partial waves, each partial wave of the conserved total angular momentum is split into two partial waves of the orbital angular momentum in a manner consistent with the conservation of the total angular momentum quantum number.     

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

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.     

Spectral Sum Rules for the Circular Aharonov-Bohm Quantum Billiard

This work presents the results of a quantitative investigation of the “sum rule method” recently proposed by the author for calculating low-lying energy levels. The system considered in detail is the circular Aharonov-Bohm quantum billiard recently introduced by Berry and Robnik. Exact, expressions are derived for the spectral zeta function at positiveinteger values as a function of the magnetic flux. Using the zeta function for fixed angular momentum, we observe a very fast convergence to the exact ground state energy (“precocious convergence”).     

Negative refraction and quantum vacuum effects in gyroelectric chiral medium and anisotropic magnetoelectric material

Some nontrivial effects (negative refraction and quantum vacuum effects) in gyroelectric chiral medium and magnetoelectric material are studied. It is shown that the refractive indices corresponding to some of the eigen modes in the gyroelectric chiral medium and magnetoelectric material may have negative real parts since both the gyroelectric and magnetoelectric parameters can dramatically reduce the refractive indices in certain frequency bands. As an anisotropic electromagnetic environment could be created due to the breaking of universal symmetry of vacuum mode distribution (and hence the noncompensation effect of a pair of counter‐propagating vacuum modes arises) inside the magnetoelectric material, the quantum vacuum in such an anisotropic electromagnetic environment may have a nonzero angular momentum. A novel quantum vacuum effect (angular momentum transfer between the quantum vacuum and the anisotropic magnetoelectric material) that may accompany the effect of magnetoelectric negative refraction is suggested. Such a nontrivial effect can be utilized to design sensitive, accurate measurement techniques, e.g., nanoscale‐sensitivity sensor.     

电磁学与电动力学中的磁单极-I

本文及后继三篇文章在电磁学和电动力学框架内分别介绍磁单极的若干奇特性质.针对由一个磁单极和一个点电荷构成的体系,首先证明这个体系的电磁场角动量具有极简洁的表达式并讨论可能的电荷量子化,然后显式地演示体系角动量的转化与守恒.     

Information (no-energy) waves described by global potentials

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.     

量子环上的负电荷激子

讨论了负电荷激子X^-的能-光谱及其Aharonov-Bhom振荡.负电荷激子是三个带电粒子组成的体系,其基函数（基矢）数目大,数值计算艰巨. 以往人们常把体系的空间波函数分离成质心运动和相对运动两部分来处理,这种方法误差大,只适用于外加磁场很小的情况.直接由体系的Hamilton量出发,基于角动量守恒,把基矢按总角动量分类. 据此提出了一种简便的求解体系的本征矢和本征函数方案,使用该方法使计算时间节省了90%以上.所得计算结果没有抗磁现象,且计算结果与现有的实验数据符合很好.还讨论了环的半径、介质电容率和空穴的有效质量与ABO的关系. 关键词： 量子环 负电荷激子 能-光谱 Aharonov-Bhom振荡     

Angular momentum density of a Gaussian vortex beam

The Gaussian vortex beam is assumed to be linearly polarized.The analytical expression of the electric field of a linearly polarized Gaussian vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integral formulae.The propagating magnetic field of the linearly polarized Gaussian vortex beam is presented by taking the curl of the electric field.By employing the electromagnetic field of the linearly polarized Gaussian vortex beam beyond the paraxial approximation,the analytical expression of the angular momentum density of the linearly polarized Gaussian vortex beam is derived.The three components of the angular momentum density of a linearly polarized Gaussian vortex beam are demonstrated in the reference plane.The effects of the linearly polarized angle and the topological charge on the three components of the angular momentum density are investigated.To acquire the more longitudinal angular momentum density requires such an optimal choice that the linearly polarized angle is set to be zero and the topological charge increases.This research is useful to the optical trapping,the optical guiding,and the optical manipulation.