Gravitational Aharonov-Bohm Effect

We study a purely gravitational Aharonov-Bohm effect. The space-time curvature is concentrated in the quasiregular singularity of a cosmic string, outside of which space-time is (locally) flat. The symmetries of this field configuration are described by the groupoid symmetries rather than by the usual group symmetries. The groupoid in question is formed by homotopy classes of piecewise smooth paths in the cosmic string region. A gravitational counterpart of the Aharonov-Bohm effect occurs if the symmetry of the system, with respect to the groupoid action, is broken down.     

Quantum Processes beyond the Aharonov-Bohm Effect

We consider QED processes in the presence of an infinitely thin and infinitely long straight string with a magnetic flux inside it. The bremsstrahlung from an electron passing by the magnetic string and the electron-positron pair production by a single photon are reviewed. Based on the exact electron and positron solutions of the Dirac equation in the external Aharonov-Bohm potential we present matrix elements for these processes. The dependence of the resulting cross sections on energies, directions, and polarizations of the involved particles is discussed for low energies.     

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.     

Topological Aharonov-Bohm Effect and Pseudo-Particle Bundles

Exploiting a topological approach, we discuss the outstanding Aharonov-Bohm effect and try to explain it in the context of the principal \(P(\mathcal {M}, \mathrm {U}(1))\) bundle. We show that this could be done by excluding a specific region from the main manifold which acts as the solenoid around which the effect is observed. Moreover, we discuss the impacts of pseudo-particles in this topological approach.     

A mathematical model for the Aharonov-Bohm effect

In this paper, we show that a unitary representation of the covering group of the Euclidean group E₂ of the plane is a good mathematical model for the Aharonov-Bohm effect: We obtain the Hamiltonian as the representative of the Casimir of the Lie algebra of E₂ and we explain the shift in the phase difference between the two beams in the interference experiment of Aharonov-Bohm.     

A short note on the Aharonov-Bohm effect

We point out that the Aharonov-Bohm effect is a 4-dimensional nonlocal geometric phenomenon. We give two examples which in 3 dimensions appear rather mysterious, but which are easily understood in 4 dimensions. We also discuss why it is integrated effects over fields (potentials) rather than the fields themselves that are important.     

Homotopy and Path Integrals in the Time-dependent Aharonov-Bohm Effect

For time-independent fields the Aharonov-Bohm effect has been obtained by idealizing the coordinate space as multiply-connected and using representations of its fundamental homotopy group to provide information on what is physically identified as the magnetic flux. With a time-dependent field, multiple-connectedness introduces the same degree of ambiguity; by taking into account electromagnetic fields induced by the time dependence, full physical behavior is again recovered once a representation is selected. The selection depends on a single arbitrary time (hence the so-called holonomies are not unique), although no physical effects depend on the value of that particular time. These features can also be phrased in terms of the selection of self-adjoint extensions, thereby involving yet another question that has come up in this context, namely, boundary conditions for the wave function.     

Remark on the Connectedness of Space in the Experimental Devices of Aharonov-Bohm Effect

This article shows that in Aharonov-Bohm (AB) effect arrangements, the electron wave propagation spaceis doubly connected for two real coherent sources, and simply connected under certain condition for two virtual coherentsources, and all known AB experiments belong to the latter case. By the Feynman path integral method, we show thatin the former case there is no AB effect, whereas in the latter case there is.     

Remark on the Connectedness of Space in the Experimental Devices of Aharonov-Bohm Effect

This article shows that in Aharonov-Bohm (AB) effect arrangements, the electron wave propagation space is doubly connected for two real coherent sources, and simply connected under certain condition for two virtual coherent sources, and all known AB experiments belong to the latter case. By the Feynman path integral method, we show that in the former case there is no AB effect, whereas in the latter case there is.     

Optical Aharonov-Bohm Effect: An Inverse Hyperbolic Problems Approach

We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary measurements. We interpret the inverse problem result as a possibility in principle to detect the optical Aharonov-Bohm effect by the boundary measurements.     

Effect of the Aharonov-Bohm flux on the magnetic gap soliton in antiferromagnetic chain

Employing the double-sublattice, the coherent state ansatz, and the time-dependent variational principle, we have studied the effects of the Aharonov-Bohm flux on the soliton in one-dimensional antiferromagnetic chain. The results show that the Aharonov-Bohm flux have an effect on the peak, the width, the energy and the spatial configuration of the spin of the soliton.     

Topological Aharonov-Bohm Effect of Neutral Scalar Particle on Noncommutative Space

We study the interactions between a neutral scalar particle and electromagnetic fields on noncommutative space. Because of the noncommutativity of space, neutral particle can couple to electromagnetic fields at the tree level, and the interaction strength is represented by a new coupling constant. We find that on noncommtuative space the topological Aharonov-Bohm effect is nontrivial even for neutral scalar particle.     

Macroscopic test of the Aharonov-Bohm effect

The Aharonov-Bohm (AB) effect is a purely quantum mechanical effect. The original (classified as type-I) AB-phase shift exists in experimental conditions where the electromagnetic fields and forces are zero. It is the absence of forces that makes the AB effect entirely quantum mechanical. Although the AB-phase shift has been demonstrated unambiguously, the absence of forces in type-I AB effects has never been shown. Here, we report the observation of the absence of time delays associated with forces of the magnitude needed to explain the AB-phase shift for a macroscopic system.     

Classical origins of the Aharonov-Bohm effect

It is shown, in a large variety of manifestations, that the Aharonov—Bohm effect has classical counterparts in aspects concerning energy and momentum balance. No counterexamples are found in the cases considered, although whenever image charges shield the magnetic field region from the electric field of the passing electron the classical momentum effects, while present, would not be observable. Similarly, if the magnetic flux is maintained by superconductors, magnetic shielding will also render the classical energy effect unobservable. Partial shieldings of either type will reduce but not totally eliminate the corresponding observable classical manifestations of these effects.     

High-Velocity Estimates for the Scattering Operator and Aharonov-Bohm Effect in Three Dimensions

We obtain high-velocity estimates with error bounds for the scattering operator of the Schrödinger equation in three dimensions with electromagnetic potentials in the exterior of bounded obstacles that are handlebodies. A particular case is a finite number of tori. We prove our results with time-dependent methods. We consider high-velocity estimates where the direction of the velocity of the incoming electrons is kept fixed as its absolute value goes to infinity. In the case of one torus our results give a rigorous proof that quantum mechanics predicts the interference patterns observed in the fundamental experiments of Tonomura et al. that gave conclusive evidence of the existence of the Aharonov-Bohm effect using a toroidal magnet. We give a method for the reconstruction of the flux of the magnetic field over a cross-section of the torus modulo 2π. Equivalently, we determine modulo 2π the difference in phase for two electrons that travel to infinity, when one goes inside the hole and the other outside it. For this purpose we only need the high-velocity limit of the scattering operator for one direction of the velocity of the incoming electrons. When there are several tori-or more generally handlebodies-the information that we obtain in the fluxes, and on the difference of phases, depends on the relative position of the tori and on the direction of the velocities when we take the high-velocity limit of the incoming electrons. For some locations of the tori we can determine all the fluxes modulo 2π by taking the high-velocity limit in only one direction. We also give a method for the unique reconstruction of the electric potential and the magnetic field outside the handlebodies from the high-velocity limit of the scattering operator.     

Mathematical Justification of the Aharonov-Bohm Hamiltonian

It is presented, in the framework of nonrelativistic quantum mechanics, a justification of the usual Aharonov-Bohm hamiltonian (with solenoid of radius greater than zero). This is obtained by way of increasing sequences of finitely long solenoids together with a natural impermeability procedure; further, both limits commute. Such rigorous limits are in the strong resolvent sense and in both ?² and ?³ spaces.     

Effect of the Aharonov-Bohm Potential on the Optical Polaron Soliton Motion in One-Dimensional Rings

The effect of the Aharonov-Bohm potential on the optical polaron solitons is considered by making use of vibration configuration resulting from the energy minimum. Two new polaron solutions with solitary wave form and their relevant properties have been obtained. The results show that the soliton's shape, location, self-trapping energy and effective mass depend on the Aharonov-Bohm dux. At the same time, the bell solitons appear at the polaron energy band, while the kink excitation at the top.