Dyon condensation and the Aharonov-Bohm effect

We derive the string representation of the Abelian Higgs theory in which dyons are condensed. It happens that in such a representation the topological interaction exists in the expectation value of the Wilson loop. Due to this interaction the dynamics of the string spanned on the Wilson loop is nontrivial. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 6, 367–371 (25 March 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

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.     

Conservation laws and the electric Aharonov-Bohm effect

The original derivation of the electric Aharonov-Bohm effect is analysed. It is shown that the operation of a simple device based upon the principles used in that derivation is incompatible with the law of energy conservation. It is concluded that the original proof of the effect is incorrect.     

The optical Aharonov-Bohm effect

It is shown that the vector potential of a circularly polarized laser causes the optical equivalent of the Aharonov-Bohm effect. An estimate is made of the expected fringe shift due to a circularly polarized laser directed through an optical fiber in an electron diffraction experiment, and it is shown that the effect is equivalent to that of a magnetic field.     

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.     

Topological shifts in the Aharonov-Bohm effect

The topological nature of the Aharonov-Bohm effect is examined. The interference terms are found to contain the usual flux dependent shift as the dominant observable effect and an additional topological shift unnoticeable in the two-slit interference experiment.     

Locality and topology in the molecular Aharonov-Bohm effect

It is shown that the molecular Aharonov-Bohm effect is neither nonlocal nor topological in the sense of the standard magnetic Aharonov-Bohm effect. It is further argued that there is a close relationship between the molecular Aharonov-Bohm effect and the Aharonov-Casher effect for an electrically neutral spin -1 / 2 particle encircling a line of charge.     

On the nature of the Aharonov-Bohm effect

It is shown that zero-field potentials may be responsible for the Aharonov-Bohm effect. A magnetic field B=curlA ^f has a physical (gauge-invariant) meaning for field potentials A ^f, whereas a circulation ∮_C A ⁰ d r has a physical meaning for zero-field potentials A ⁰.     

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.     

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.     

Aharonov-Bohm effect in the superconducting LOFF state

We study the Aharonov-Bohm oscillations of the transition temperature, paraconductivity, and specific heat of a thin ring in the regime of the inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell superconducting state. We found that, in contrast to the uniform superconductivity, the magnetic flux might increase the critical temperature of the Larkin-Ovchinnikov-Fulde-Ferrell state. The degeneracy of the inhomogeneous superconducting state reveals in a double peak structure of the Aharonov-Bohm oscillations. The text was submitted by the authors in English.     

Aharonov-Bohm effect in the presence of superconductors

The analysis of a previous paper, in which it was shown that the energy for the Aharonov-Bohm effect could be traced to the interaction energy between the magnetic field of the electron and the background magnetic field, is extended to cover the case in which the magnetic field of the electron is shielded from the background magnetic field by a superconducting material. The paradox that arises from the fact that such a shielding would apparently preclude the possibility of an interaction energy is resolved and, within the limits of the ideal situation considered, the observed experimental result is derived.     

Aharonov-Bohm effect in spherical billiard

Using Gutzwiller's periodic orbit theory, we study the quantum level density of a spherical billiard in the presence of a magnetic flux line added at its center, especially discuss the influence of the magnetic flux strength on the quantum level density. The Fourier transformed quantum level density of this system has allowed direct comparison between peaks in the level density and the length of the periodic orbits. For particular magnetic flux strength, the amplitude of the peaks in the level density decreased and some of the peaks disappeared. This result suggests that Aharonov-Bohm effect manifests itself through the cancellation of periodic orbits. This phenomenon will provide a new experimental testing ground for exploring Aharonov-Bohm effect.