On the possibility of transmitting signals by means of the Aharonov-Bohm effect

A mental experiment on the possible effect of an alternating current flowing along generating lines of an infinitely long cylinder on the interference diffraction pattern of microparticles has been considered. The possibility of exciting and detecting electromagnetic waves, which correspond to a zero electromagnetic field, and transmitting signals by means of the Aharonov-Bohm effect changing the phase of the electron wave function has been discussed. The results can be used in the design of a detector of an electromagnetic field that does not absorb photons of the detected radiation.     

When is the wave function single-valued?

It is shown that single-valuedness of the wave function can be lost because of an external field approximation. The Aharonov-Bohm effect is studied in detail as an example of the problem. Specifically, it is shown that the solenoid (represented as a rotating, charged cylinder) has a wave function that undergoes a phase shift equal in magnitude, but with opposite sign, to the phase shift suffered by the electron's wave function when the electron passes the solenoid.     

Radiation of scalar waves by the discontinuities in the antenna geometries

The electrical scalar potential satisfies the Helmholtz equation for time-harmonic waves and Aharonov-Bohm showed that the electromagnetic potentials have physical reality. For these reasons, the scalar potential represents scalar wave propagation in space. The gradient of the scalar wave leads to the electric field intensity, but it does not create the magnetic field. The criteria for the radiation of the scalar waves are studied on various linear antennas. The radiation integrals of the antennas are evaluated asymptotically by taking into account the edge effects. The radiation diagrams are plotted numerically and the phase velocities of the scalar waves are investigated in the near field.     

基于麦克斯韦方程的交变电流长螺线管磁场

为了分析方波驱动长螺线管内磁场畸变机理,利用麦克斯韦方程研究了螺线管内外的磁场分布情况。首先,利用麦克斯韦方程,分别建立了正弦波驱动螺线管内外电场、磁场模型,并结合安培环路定律和电磁感应定律选取了合适的边界条件,得到了正弦波驱动长螺线管的磁场分布;其次,通过傅里叶变换将方波信号变换为多个正弦信号叠加的形式,从而得到了方波驱动长螺线管磁场分布;最后,通过仿真试验重点分析了方波驱动信号频率对磁场的影响,并得出结论:方波驱动长螺线管磁场波形会失真、畸变,驱动信号频率较低、距离螺线管轴线距离较近处,磁场的方波特性较好。     

The Maxwell-Lodge effect: Significance of electromagnetic potentials in the classical theory

The Aharonov-Bohm effect has been the starting point of the reconsideration of the reality of the vector potential within quantum physics. We argue that the Maxwell-Lodge effect is its classical equivalent: what is the origin of the electromotive force induced in a coil surrounding a (finite) solenoid fed by an alternative current? We demonstrate theoretically, experimentally and numerically that the effect can be understood using the vector potential while it cannot using only the fields.     

Aharonov-Bohm scattering of a wave packet of finite extension

The scattering of an electron from a thin, shielded solenoid (Aharonov-Bohm effect) is studied by means of the time-dependentGreen's function of the problem. The structure of theGreen's function reveals in a lucid way the nonidentity of canonical and kinetic angular momentum as the origin of the Aharonov-Bohm scattering. The time development of a Gaussian wave packet is studied in some detail to investigate the validity of certain objections against the original work ofAharonov andBohm. In an appendix some results are given for the case of finite radius of the solenoid and finite shielding potential.     

Aharonov-Bohm effect revisited

The Aharonov-Bohm (AB) effect shows that electromagnetic potentials can influence an electron in a field-free region. The single-slit and double-slit electron diffraction patterns are explicitly calculated here by the Feynman path integral method for different configurations of the magnetic field in order to compare the effect of the vector potential with the effect of the magnetic field. When an electron passes through a magnetic field behind the slits, the whole diffrection pattern is shifted due to the Lorentz force. When an electron passes through two slits with magnetic flux confined to a small cylinder between them, the double-slit diffraction pattern is shifted within the single-slit diffraction envelope. The asymmetric diffraction pattern corresponds to a nonzero average displacement and momentum of the electron even though the field exerts no force on the electron. This behavior can be understood on the basis of a quantum-mechanical interference effect. The classical limit of the electron diffraction patterns is taken to obtain the classical particle distributions. The effect of the potential vanishes in the classical limit, while the effect of the magnetic field persists because of the Lorentz force.     

Momentum-transfer scattering cross section and the Aharonov-Bohm effect on a toroidal solenoid

The quantum-mechanical Aharonov-Bohm effect in the diffraction of charged particles by a toroidal solenoid containing a magnetic field is investigated. The total and differential elastic scattering cross sections depend on the magnetic flux inside the solenoid, even in the presence of a “black” ring-shaped screen which prevents charged particles from entering the region where the magnetic field is localized. Relations describing the momentum-transfer cross section for the elastic scattering of charged particles by a toroidal solenoid are obtained in the eikonal approximation and in a unitary model of scattering with a sharp jump in the partial amplitudes. The momentum-transfer scattering cross section is proportional to the average transfer of the longitudinal momentum of the scattered particle and can be expressed in terms of a force operator. It is shown that in the absence of a screen the momentum-transfer scattering cross section of toroidal solenoid is indeed determined only by the part of the incident beam that intersects the inner region of the toroidal solenoid, where the magnetic field intensity and, therefore, the Lorentz force are nonzero. At the same time, the momentum-transfer cross section for the scattering of charged particles by a toroidal solenoid covered by a “black” ring-shaped screen does not depend on the magnetic flux inside the solenoid and is identical to the momentum-transfer cross section for diffraction by the same screen. The contribution from scattering by an opening in the screen, which depends on the magnetic flux, is completely compensated by the contribution of the interference of the scattering amplitudes of the opening and the “black” screen.     

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.     

The Aharonov-Bohm effect for nonstationary quasiclassical trajectory-coherent states in a uniform magnetic field

Approximate (as h 0) dynamic states in the form of nondiffusing wave packets, localized in the vicinity of a classical trajectory (nonintersecting the solenoid), quasiclassical nonstationary trajectory-coherent states, are constructed for nonrelativistic electron motion in a uniform magnetic field in the presence of an infinitely thin and long solenoid. The occurrence of the Aharonov-Bohm effect in such states is investigated. Special cases of electron motion — in a uniform magnetic field and in the solenoid field — are considered.Moscow Institute of Electronic Machinery. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 83–90, October, 1992.     

Optical theorem and Aharonov-Bohm scattering

A rigorous derivation of the optical theorem (OT) from the conservation of probability flux (CPF) is presented for scattering on an arbitrary spherically symmetric potential inN-spatial dimensions (ND). The constructed expression for the OT is found to yield the corresponding well-known results for two- and three-dimensional cases in a rather natural way. The Aharonov-Bohm (AB) effect is considered as a scattering event of an electron by a magnetic field confined in an infinitely long shielded solenoid and a similar derivation is attempted for an appropriate optical theorem. Our current understanding of the scattering theory is found to be inadequate for the purpose. The reason for this is discussed in some detail.     

Bound on the photon charge from the phase coherence of extragalactic radiation

If the photon possessed a nonzero charge, then electromagnetic waves traveling along different paths would acquire Aharonov-Bohm phase differences. The fact that such an effect has not hindered interferometric astronomy places a bound on the photon charge estimated to be at the 10(-32)e level if all photons have the same charge and 10(-46)e if different photons can carry different charges.     

On a Hypothetical Explanation of the Aharonov-Bohm Effect

I study in detail a proposal made by T. H. Boyer in an attempt to explain classically the Aharonov-Bohm (AB) effect. Boyer claims that in an AB experiment, the perturbation the external incident particle produces on the charge and current distributions within the solenoid will affect back the motion of the external particle. With a qualitative analysis based on energetic considerations, Boyer seemed to arrive at the conclusion that this perturbation could give account of the AB effect. In this paper I make explicit calculations which show that Boyer's conjecture fails. Indeed I find that the perturbation produced on the solenoid, and then its effect on the external charge, is independent of the solenoid current and consequently cannot account for the AB effect, which is current dependent.     

The Kaluza-Klein theory and four-dimensional spacetime

The conventional electromagnetism, which includes Maxwell's field equations and the Lorentz force relation, does not provide an explanation of well-known electromagnetic phenomena, such as the Aharonov-Bohm interference effect and the Meissner-Ochsenfeld effect in superconductors. In this paper, it is shown that the Kaluza-Klein five-dimensional theory suggests a simple explanation of these effects on a unified basis.     

The Electromagnetic Sector of the Evans Field Theory

The equations of the electromagnetic sector of the Evans field theory are given in terms of differential geometry and are based on the well-known structure relations and Bianchi identities. The equations thus complete Einstein’s basic axiom, that physics is derived from geometry, and extend the axiom to electrodynamics. Precise tests are suggested for the theory using the interaction of circularly polarized electromagnetic radiation with a non-relativistic electron beam. These tests include; the inverse Faraday effect (IFE), radiatively induced fermion resonance (RFR), and the electromagnetic Aharonov-Bohm (EMAB) effect.     

New relativistic gravitational effects using charged-particle interferometry

A new class of gravitational effects, in the quantum interference of charged particles, are studied in electron interferometry and superconducting Josephson interferometry. These include phase shifts due to the gravitationally induced Schiff-Barnhill field, rotationally induced London moment, and the modification of the Aharonov-Bohm type of phase shifts, due to the general relativistic coupling of the electromagnetic field to the gravitational field. These effects are interesting, even from a purely theoretical point of view, because they involve an elegant interplay between gravitation, electromagnetism, and quantum mechanics. But new predictions are also made which, if confirmed, would provide the first observation of relativistic gravitational effects, involving the electric charge, at the quantum mechanical level. The possibility of using these effects to detect gravitational waves is also discussed.This essay received the first award from the Gravity Research Foundation for the year 1983-Ed.     

磁力提升装置样机的数值分析与实验研究

研制的磁力提升装置实现了对加速器驱动次临界系统(ADS)新型钨基合金球靶材的电磁提升。其基本原理是通过控制一组螺线管的加电时序,实现磁场的移动,移动磁场作用于靶材完成其输运。螺线管作为该装置的主要部件,其结构影响电磁提升的效率。为优化其结构,采用Ansys Maxwell分析螺线管的磁场分布,确定螺线管结构。同时利用Ansys Maxwell给每个螺线管加不同宽度的脉冲进行数值模拟,通过调节每个螺线管的通断电时间和同时工作的螺线管单元数,模拟计算合金球的受力。在数值模拟的基础上完成了磁力提升装置样机的加工和实验研究,实现了钨基合金球输运的预期效果。     

Ether drift experiments and electromagnetic momentum

Propagation of Aharonov-Bohm matter waves and light waves in moving media is characterized by the interaction electromagnetic momentum. Thus, recent models of light propagation in moving rarefied media justify and call for an optical experiment of the Mascart-Jamin type, capable of testing the modern interpretations of ether drift experiments.     

Born-Oppenheimer近似下谐振子场驱动电磁模系统的Berry相和Hannay角

研究了Born-Oppenheimer近似下谐振子场驱动电磁模系统的Berry相和Hannay角, 通过理论计算得到了其表达式, 并讨论了这二者之间的半经典关系.结果表明, 这一量子Born-Oppenheimer复合系统的Berry相包含两部分: 第一部分与通常几何相的定义相同, 另一项则是由耦合造成的有效规范式引入的.这一量子修正可以被看作一个等效的Aharonov-Bohm效应.不仅如此, 其对应经典系统的Hannay角的定义中也存在类似的现象. 由此可见, 这一复合系统的Berry相与Hannay角之间也存在半经典关系, 并与文献[16] 中通常情况下的半经典关系相同.此外, 上述理论也可以运用于解决产生中性原子的人造规范势等物理问题. 关键词： Berry相 Hannay角 量子经典对应 Born-Oppenheimer近似