The Aharonov-Bohm Effect: An Exploration of Quantum Interference and Electromagnetic Potentials

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 Φ through the solenoid induces a phase shift in the electron’s wave function.This phase shift,quantified by △φ=qΦ/hc,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.

Photon Structure and Wave Function from the Vector Potential Quantization

A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.

Moist Potential Vorticity Vector for Diagnosis of Heavy Rainfall Events in Tanzania

In this paper, we modify the convective vorticity vector (CVV) defined as a cross product of absolute vorticity and gradient of equivalent potential temperature to moist potential vorticity vector (MPVV) defined as a cross product of absolute vorticity () and the gradient of the moist-air entropy potential temperature (). The patterns of (MPVV) are compared with the patterns of heavy rainfall events that occurred over different regions in Tanzania on 20th to 22nd December, 2011 and on 5th to 8th May, 2015. Moreover, the article aimed at assessing the relative contributions of the magnitude, horizontal and vertical components of (MPVV) detecting on the observed patterns of rainfall events. Dynamic and thermodynamic variables: wind speed, temperature, atmospheric pressure and relative humidity from numerical output generated by the Weather Research and Forecasting (WRF) model running at Tanzania Meteorological Agency (TMA) were used to compute MPVV. It is found that MPVV provide accurate tracking of locations received heavy rainfall, suggesting its potential use as a dynamic tracer for heavy rainfall events in Tanzania. Finally it is found that the first and second components of MPVV contribute almost equally in tracing locations received heavy rainfall events. The magnitude of MPVV described the locations received heavy rainfall events better than the components.

Spin Supercurrent in Phenomena of Quantum Non-Locality (Quantum Correlations, Magnetic Vector Potential) and in Near-Field Antenna Effect

It is shown that such phenomena as quantum correlations (interaction of space-separated quantum entities), the action of magnetic vector potential on quantum entities in the absence of magnetic field, and near-field antenna effect (the existence of superluminally propagating electromagnetic fields) may be explained by action of spin supercurrents. In case of quantum correlations between quantum entities, spin supercurrent emerges between virtual particles pairs (virtual photons) created by those quantum entities. The explanation of magnetic vector potential and near-field antenna effect is based on contemporary principle of quantum mechanics: the physical vacuum is not an empty space but the ground state of the field consisting of quantum harmonic oscillators (QHOs) characterized by zero-point energy. Using the properties of the oscillators and spin supercurrent, it is proved that magnetic vector potential is proportional to the moment causing the orientation of spin of QHO along the direction of magnetic field. The near-field antenna effect is supposed to take place as a result of action of spin supercurrent causing secondary electromagnetic oscillations. In this way, the electromagnetic field may spread at the speed of spin supercurrent. As spin supercurrent is an inertia free process, its speed may be greater than that of light, which does not contradict postulates of special relativity that sets limits to the speed of inertial systems only.

MHD Equilibrium with Reversed Current Density and Magnetic Islands Revisited:the Vacuum Vector Potential Calculus

The solution of Grad-Shafranov equation determines the stationary behavior of fusion plasma inside a tokamak. To solve the equation it is necessary to know the toroidal current density profile. Recent works show that it is possible to determine a magnetohydrodynamic （MHD） equilibrium with reversed current density （RCD） profiles that presents magnetic islands. In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.

Approximate solution of the spin-one Duffin-Kemmer-Petiau(DKP) equation under a non-minimal vector Yukawa potential in(1+1)-dimensions

We solve the Duffin-Kemmer-Petiau （DKP） equation with a non-minimal vector Yukawa potential in （1＋1）- dimensional spa^e-time for spin-1 particles. The Nikiforov Uvarov method is used in the calculations, and the eigen- functions as well as the energy eigenvalues are obtained in a proper Pekeris-type approximation.

Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.

Pulsed Vector Magnetic Potential Field Existence

Experimental confirmation discussed the effect of the immediate surroundings of a pulse-powered toroidal coil on biological material which was placed in an environment without the influence of electromagnetic force.

Symbolic Computation and Graphic Presentation of Magneto-Static Field and Its Associated Vector Potential for a Steady Looping Current

With the advent of Computer Algebra System (CAS) such as Mathematica [1], challenging symbolic longhand calcula-tions can effectively be performed free of error and at ease. Mathematica’s integrated features allow the investigator to combine the needed symbolic, numeric and graphic modules all in one interactive environment. This assists the author to focus on interpreting the output rather than exerting the efforts of relating the scattered separate modules. In this note the author, utilizing these three features, explores the magneto-static field and its associated vector potential of a steady looping current. In particular by deploying the numeric features of Mathematica the exact value of the vector potential of the looping current conducive to its 3D graph is presented.

Generalization of the Second Order Vector Potential Formulation for Arbitrary Non-Orthogonal Curvilinear Coordinates Systems from the Covariant Form of Maxwell's Equations

A great number of semi-analytical models, notably the representation of electromagnetic fields by integral equations are based on the second order vector potential (SOVP) formalism which introduces two scalar potentials in order to obtain analytical expressions of the electromagnetic fields from the two potentials. However, the scalar decomposition is often known for canonical coordinate systems. This paper aims in introducing a specific SOVP formulation dedicated to arbitrary non-orthogonal curvilinear coordinates systems. The electromagnetic field representation which is derived in this paper constitutes the key stone for the development of semi-analytical models for solving some eddy currents moelling problems and electromagnetic radiation problems considering at least two homogeneous media separated by a rough interface. This SOVP formulation is derived from the tensor formalism and Maxwell’s equations written in a non-orthogonal coordinates system adapted to a surface characterized by a 2D arbitrary aperiodic profile.

Gradient Transformation of Momentum and Single-Valued Vector Potential in Nonrelativistic Dynamics

A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution of the corresponding homogeneous equation that does not change the Lagrange equations. When dynamics is described by momenta and coordinates, this transformation is not the vector potential modification, which does not change expressions for other physical quantities, but a canonical transformation of momentum, which changes expressions for all fimctions of momentum, not changing the Poisson brackets, and, hence, the integrals of motion. The generating function of this transformation must reverse sign under the time-charge reversal. In quantum mechanics the unitary transformation corresponds to this canonical transformation. It also does not change the commutation relations. The phase of this unitary operator also must reverse sign under the time-charge reversal. Examples of necessary vector potentials for some magnetic fields are presented.

Bio-Electromagnetics without Fields: The Effect of the Vector Potential

Numerous considerations deal with specialties of bioelectromagnetic effects, including the force-free and field-free interactions. The fact that bioelectromagnetic phenomena consist of effects without mechanical forces and even without measurable fields looks impossible in the simple considerations. However, the stochastic fluctuations cause surprising results, with scientifically proven bioelectromagnetism in field-free conditions. In the first steps, we show the scalar and vector potentials’ specialties instead of electric and magnetic fields defined by the well-known Maxwellian equations. The vanishing of the fields is connected to the potentials’ stochastic fluctuations, the noises control the “zero-ground”. The result shows a possibility of a wave that has no attenuation during its transmission through the material. In this meaning, the result is similar to the consequences of the scalar-wave (SW) considerations. The structural changes follow a particular noise spectrum (called pink-noise or 1/f noise), which keeps the entropy constant in a broad range of scaling magnification.

Exact Solutions of the Klein-Gordon Equation with a New Anharmonic Oscillator Potential

We solve the Klein-Cordon equation with a new anharmonic oscillator potential and present the exact solutions. It is shown that under the condition of equal scalar and vector potentials, the Klein-Cordon equation could be separated into an angular equation and a radial equation. The angular solutions are the associated-Legendre polynomial and the radial solutions are expressed in terms of the confluent hypergeometric functions. Finally, the energy equation is obtained from the boundary condition satisfied by the radial wavefunctions.

Real-time rear-end crash potential prediction on freeways

This study develops new real-time freeway rear-end crash potential predictors using support vector machine(SVM) technique. The relationship between rear-end crash occurrences and traffic conditions were explored using historical loop detector data from Interstate-894 in Milwaukee, Wisconsin, USA. The extracted loop detection data were aggregated over different stations and time intervals to produce explanatory features. A feature selection process, which addresses the interaction between SVM classifiers and explanatory features, was adopted to identify the features that significantly influence rear-end crashes. Afterwards, the identified significant explanatory features over three separate time levels were used to train three SVM models. In the end, the multi-layer perceptron(MLP) artificial neural network models were used as benchmarks to evaluate the performance of SVM models. The results show that the proposed feature selection procedure greatly enhances the accuracy and generalization capability of SVM models. Moreover, the optimal SVM classifier achieves 81.1% overall prediction precision rate. In comparison with MLP artificial neural networks, SVM models provide better results in terms of crash prediction accuracy and false positive rate, which confirms the superior performance of SVM technique in rear-end crash potential prediction analysis.

A Review of Potential Vorticity and Its Possible Application in the Moist Atmospheric Flow

Potential vorticity (PV) has been served as a powerful and useful dynamic tracer for the understanding of the large-scale dynamics and synoptic variations in the atmosphere and oceans.Significant progress has been made on the application of PV.In recent decades there has been a substantial amount of work done on PV in a gen-eral moist atmosphere.In this paper PV and the general-ized moist potential vorticity (GMPV) and their applica-tion in the tropical cyclones and mesoscale meteorologi-cal field are reviewed.The GMPV is derived for a real atmosphere (neither totally dry nor saturated) by intro-ducing a generalized potential temperature instead of the potential temperature or equivalent potential temperature.Such a generalization can depict the moist effect on PV anomaly in the non-uniformly saturated atmosphere.A new convective vorticity vector (CVV) is introduced in connection with GMPV in order to diagnose the devel-opment of tropical deep convections.

Influence of stimuli color on steady-state visual evoked potentials based BCI wheelchair control

In recent years, Brain Computer Interface (BCI) systems based on Steady-State Visual Evoked Potential (SSVEP) have received much attention. This study tries to develop a SSVEP based BCI system that can control a wheelchair prototype in five different positions including stop position. In this study four different flickering frequencies in low frequency region were used to elicit the SSVEPs and were displayed on a Liquid Crystal Display (LCD) monitor using Lab-VIEW. Four stimuli colors, green, red, blue and violet were used to investigate the color influence in SSVEPs. The Electroencephalogram (EEG) signals recorded from the occipital region were segmented into 1 second window and features were extracted by using Fast Fourier Transform (FFT). One-Against-All (OAA), a popular strategy for multiclass SVM, is used to classify SSVEP signals. During stimuli color comparison SSVEP with violet color showed higher accuracy than that with green, red and blue stimuli.

The Potential-Vortex Theory of Electromagnetic Waves

An electromagnetic wave is a complex vortex and a potential process. This allows us to omit the Lorentz gauge, formulate a mathematically precise theory, and avoid physics discordances. The mechanism of distribution of complex waves in dielectric and electrical conductive environments was described.

Decomposition of Noncommutative U(1)Gauge Potential

We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor

A neutral point potential drift control method for NPC three-level inverter

The output current harmonic distortion of a three-level inverter is less than the traditional twolevel inverter.The voltage stress of the semiconductor switch is low.A neutral point potential drift control method is proposed to solve the problem of the neutral point potential drift of the three-level inverter.The interaction mechanism between the neutral point potential and the space voltage vector is presented.The small vector output by the inverter is found to be the root cause of the midpoint potential drift.It is found that the fluctuation of the midpoint potential could be suppressed by increasing the capacitance value of the inverter bus voltage stabilizing capacitor.Furthermore,it inhibits the fluctuation of the midpoint potential.The experimental results verify the efficiency and precision of the proposed method.