Aharonov-Bohm effect revisited
Eskin, Gregory
2015-01-01
Aharonov-Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov-Bohm effect such as magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schr\\"odinger equations with Yang-Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove ...
Quantum mechanics teaches us that matter consists of waves. Interference of matter waves gives rise to delicate effects best illustrated by the double slit experiment. Aharonov and Bohm showed that the interference pattern of electrons in a multiply connected region can be influenced by magnetic fields outside that region. This surprising effect (now called the Aharonov-Bohm effect) has been measured in the laboratory. The process of understanding and coming to terms with this effect has deepened our understanding of both quantum mechanics and electromagnetism. This paper gives an elementary account of the Aharonov-Bohm effect. (author). 13 refs., 2 figs
Nonlocality of the Aharonov-Bohm effect
Aharonov, Yakir; Cohen, Eliahu; Rohrlich, Daniel
2016-04-01
Although the Aharonov-Bohm and related effects are familiar in solid-state and high-energy physics, the nonlocality of these effects has been questioned. Here we show that the Aharonov-Bohm effect has two very different aspects. One aspect is instantaneous and nonlocal; the other aspect, which depends on entanglement, unfolds continuously over time. While local, gauge-invariant variables may occasionally suffice for explaining the continuous aspect, we argue that they cannot explain the instantaneous aspect. Thus the Aharonov-Bohm effect is, in general, nonlocal.
The multisolenoid Aharonov-Bohm effect
The thesis summarizes, extends and discusses the author's achievements published in Phys. Lett. A 142, 1989, p. 5; J. Math. Phys. 32, 1991, p.13; and Phys. Lett. A 161, 1991, p. 13. The following topics are dealt with: (i) the Green function for the two-solenoid Aharonov-Bohm effect; (ii) application of Krein's formula to the multisolenoid Aharonov-Bohm effect; (iii) the scattering matrix for the two-solenoid Aharonov-Bohm effect; and (iv) the differential cross section. Reprints of the 3 publications are included. (P.A.)
About nature of Aharonov-Bohm effect
The problem on the Aharonov-Bohm effect is discussed. The method of surplus potentials for solving boundary-value problem tasks of the anisotropic media electrodynamics is considered. General notion on the vector potential in the uniaxial medium is obtained. The relationship of the zero field potentials with gauge transformation is established. The vector potential structure for the Aharonov-Bohm magnetostatic effect in particular for a solenoid with alternating current is considered. It is shown that presence of the zero field potentials in the general structure may be the cause of the Aharonov-Bohm effect
Nonlocality of the Aharonov-Bohm Effect
Aharonov, Yakir; Cohen, Eliahu; Rohrlich, Daniel
2015-01-01
Although the Aharonov-Bohm and related effects are familiar in solid state and high energy physics, the nonlocality of these effects has been questioned. Here we show, for the first time, that the Aharonov-Bohm effect has two very different aspects. One aspect is instantaneous and nonlocal; the other aspect, which depends on entanglement, unfolds continuously over time. While local, gauge-invariant variables may occasionally suffice for explaining the continuous aspect, we argue that they can...
Aharonov-Bohm effects in nanostructures
Gurtovoi, V. L.; Nikulov, A. V.; Tulin, V. A.
2009-01-01
Measurements of the Little-Parks oscillations at measuring current much lower than the persistent current give unambiguous evidence of the dc current flowing against the force of the dc electric field because of the Aharonov-Bohm effect. This result can assume that an additional force is needed for description of the Aharonov-Bohm effect observed in semiconductor, normal metal and superconductor nanostructures in contrast to the experimental result obtained recently for the case of the two-sl...
Locality and topology in the molecular Aharonov-Bohm effect
Sjöqvist, Erik
2001-01-01
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.
Tunable exciton Aharonov-Bohm effect in a quantum ring
We studied the optical Aharonov-Bohm effect for an exciton in a semiconductor quantum ring. A perpendicular electric field applied to a quantum ring with large height, is able to tune the exciton ground state energy such that it exhibits a weak observable Aharonov-Bohm oscillations. This Aharonov-Bohm effect is tunable in strength and period.
Thermoelectric effect in Aharonov-Bohm structures
Lu, Xin; Wang, Jian-Sheng; Morrel, William G.; Ni, Xiaoxi; Wu, Chang-Qin; Li, Baowen
2015-01-01
The thermoelectric effects of a single Aharonov-Bohm (SAB) ring and coupled double Aharonov-Bohm (DAB) rings have been investigated on a theoretical basis, taking into account the contributions of both electrons and phonons to the transport process by using the nonequilibrium Green's function technique. The thermoelectric figure of merit of the coupled DAB rings cannot be predicted directly by combining the values of two SAB ring systems due to the contribution of electron-phonon interaction to coupling between the two sites connecting the rings. We find that thermoelectric efficiency can be optimized by modulating the phases of the magnetic flux threading the two rings.
Thermoelectric effect in Aharonov-Bohm structures.
Lu, Xin; Wang, Jian-Sheng; Morrel, William G; Ni, Xiaoxi; Wu, Chang-Qin; Li, Baowen
2015-01-28
The thermoelectric effects of a single Aharonov-Bohm (SAB) ring and coupled double Aharonov-Bohm (DAB) rings have been investigated on a theoretical basis, taking into account the contributions of both electrons and phonons to the transport process by using the nonequilibrium Green's function technique. The thermoelectric figure of merit of the coupled DAB rings cannot be predicted directly by combining the values of two SAB ring systems due to the contribution of electron-phonon interaction to coupling between the two sites connecting the rings. We find that thermoelectric efficiency can be optimized by modulating the phases of the magnetic flux threading the two rings. PMID:25537848
The Aharonov-Bohm effect in neutral liquids
The Aharonov-Bohm effect was discovered as a quantum-mechanical effect for charged particles, but it has its counterpart in classical wave mechanics. The Aharonov-Bohm interference arises at the scattering of a sound wave by a vortex in classical and quantum hydrodynamics. This interference leads to a transverse force between quasiparticles and vortices in superfluids and superconductors. The Aharonov-Bohm effect was also generalized to neutral particles with magnetic or electric dipole momenta. The Aharonov-Bohm effect for charge particles and its modification for magnetic momenta (the Aharonov-Casher effect) have already been experimentally observed, and the efforts to detect the Aharonov-Bohm effect for electrically polarized neutral particles are on the way. A possible system for this detection is a Bose-condensate of excitons in a double quantum well. Observation of the Aharonov-Bohm effect in this system would provide direct evidence of Bose-Einstein condensation.
Locality of the Aharonov-Bohm-Casher effect
Kang, Kicheon
2014-01-01
We address the question of the locality versus nonlocality in the Aharonov-Bohm and the Aharonov-Casher effects. For this purpose, we investigate all possible configurations of ideal shielding of the overlap between the electromagnetic fields generated by a charge and by a magnetic flux, and analyze their consequences on the Aharonov-Bohm-Casher interference. In a classical treatment of shielding, the Aharonov-Bohm-Casher effect vanishes regardless of the geometry of shielding, when the local...
Aharonov-Bohm effect in spherical billiard
Dehua Wang
2007-01-01
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.
Electromagnetic potentials and Aharonov-Bohm effect
Ershkovich, Alexander
2012-01-01
Hamilton-Jacobi equation which governs classical mechanics and electrodynamics explicitly depends on the electromagnetic potentials (A,{\\phi}), similar to Schroedinger equation. We derived the Aharonov-Bohm effect from Hamilton-Jacobi equation thereby having proved that this effect is of classical origin. These facts enable us to arrive at the following conclusions: a) the very idea of special role of potentials (A,{\\phi}) in quantum mechanics (different from their role in classical physics) ...
The electric Aharonov-Bohm effect
The seminal paper of Aharonov and Bohm [Phys. Rev. 115, 485 (1959)] is at the origin of a very extensive literature in some of the more fundamental issues in physics. They claimed that electromagnetic fields can act at a distance on charged particles even if they are identically zero in the region of space where the particles propagate, that the fundamental electromagnetic quantities in quantum physics are not only the electromagnetic fields but also the circulations of the electromagnetic potentials; what gives them a real physical significance. They proposed two experiments to verify their theoretical conclusions. The magnetic Aharonov-Bohm effect, where an electron is influenced by a magnetic field that is zero in the region of space accessible to the electron, and the electric Aharonov-Bohm effect where an electron is affected by a time-dependent electric potential that is constant in the region where the electron is propagating, i.e., such that the electric field vanishes along its trajectory. The Aharonov-Bohm effects imply such a strong departure from the physical intuition coming from classical physics that it is no wonder that they remain a highly controversial issue after more than fifty years, in spite of the fact that they are discussed in most of the text books in quantum mechanics. The magnetic case has been studied extensively. The experimental issues were settled by the remarkable experiments of Tonomura et al. [Phys. Rev. Lett. 48, 1443 (1982); Phys. Rev. Lett. 56, 792 (1986)] with toroidal magnets, that gave a strong evidence of the existence of the effect, and by the recent experiment of Caprez et al. [Phys. Rev. Lett. 99, 210401 (2007)] that shows that the results of the Tonomura et al. experiments cannot be explained by the action of a force. The theoretical issues were settled by Ballesteros and Weder [Commun. Math. Phys. 285, 345 (2009); J. Math. Phys. 50, 122108 (2009); Commun. Math. Phys. 303, 175 (2011)] who rigorously proved that quantum
Aharonov--Bohm Effect in 3D Abelian Higgs Theory
Chernodub, M. N.; Gubarev, F. V.; Polikarpov, M.I.
1996-01-01
We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D Abelian Higgs Model: the corresponding topological interaction is proportional to the linking number of the vortex and the particle world trajectories. We show that the Aharonov--Bohm effect gives rise to a nontrivial interaction of tested charged particles.
Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach
Eskin, Gregory
2007-01-01
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.
Aharonov-Bohm Effect and the Supersymmetry of Identical Anyons
V. Jakubský
2010-01-01
We briefly review the relation between the Aharonov-Bohm effect and the dynamical realization of anyons. We show how the particular symmetries of the Aharonov-Bohm model give rise to the (nonlinear) supersymmetry of the two-body system of identical anyons.
The Aharonov-Bohm effect in noncommutative quantum mechanics
The Aharonov-Bohm effect in noncommutative (NC) quantum mechanics is studied. First, by introducing a shift for the magnetic vector potential we give the Schroedinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then, by solving the Schroedinger equations, we obtain the Aharonov-Bohm phase on NC space and NC phase space, respectively. (orig.)
Aharonov-Bohm Effect and the Supersymmetry of Identical Anyons
V. Jakubský
2010-01-01
Full Text Available We briefly review the relation between the Aharonov-Bohm effect and the dynamical realization of anyons. We show how the particular symmetries of the Aharonov-Bohm model give rise to the (nonlinear supersymmetry of the two-body system of identical anyons.
Photonic Aharonov-Bohm effect in photon-phonon interactions.
Li, Enbang; Eggleton, Benjamin J; Fang, Kejie; Fan, Shanhui
2014-01-01
The Aharonov-Bohm effect is one of the most intriguing phenomena in both classical and quantum physics, and associates with a number of important and fundamental issues in quantum mechanics. The Aharonov-Bohm effects of charged particles have been experimentally demonstrated and found applications in various fields. Recently, attention has also focused on the Aharonov-Bohm effect for neutral particles, such as photons. Here we propose to utilize the photon-phonon interactions to demonstrate that photonic Aharonov-Bohm effects do exist for photons. By introducing nonreciprocal phases for photons, we observe experimentally a gauge potential for photons in the visible range based on the photon-phonon interactions in acousto-optic crystals, and demonstrate the photonic Aharonov-Bohm effect. The results presented here point to new possibilities to control and manipulate photons by designing an effective gauge potential. PMID:24476790
The Aharonov-Bohm effect: Theoretical calculations and interpretations
The Aharonov-Bohm effect - the action of an external inaccessible field on the quantum state of a charged particle - is investigated in detail. An exact expression is found for the scattering amplitude of the charged particle in an infinitely long solenoid and its behavior in the shadow region is investigated. The Aharonov-Bohm effect is investigated for bound states, including Landau levels in a uniform magnetic field. It is demonstrated that the Aharonov-Bohm effect arises during the switching-on process of an external magnetic field
Two-particle Aharonov-Bohm effect in electronic interferometers
We review recent theoretical investigations on the two-particle Aharonov-Bohm effect and its relation to entanglement production and detection. The difficulties of the entanglement detection due to dephasing and finite temperature are discussed regarding a recent experimental realization of a two-particle Aharonov-Bohm interferometer [15]. We also discuss a theoretical proposal for a two-particle Aharonov-Bohm interferometer, which as against the finite bias setup is driven with dynamical single-electron sources allowing for the tunable production of time-bin entanglement.
Aharonov-Bohm Effect and Disclinations in an Elastic Medium
Furtado, Claudio; Carvalho, A. M. de M.; Ribeiro, C. A. de Lima
2006-01-01
In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov-Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov- Bohm effect. We analyze this effect in an elastic medium with one and $N$ defects.
The Aharonov-Bohm Effect in the Momentum Space
Dragoman, D.; Bogdan, S.
2005-01-01
The Schrodinger formalism of quantum mechanics is used to demonstrate the existence of the Aharonov-Bohm effect in momentum space and set-ups for experimentally demonstrating it are proposed for either free or ballistic electrons.
Photonic Aharonov-Bohm effect based on dynamic modulation.
Fang, Kejie; Yu, Zongfu; Fan, Shanhui
2012-04-13
We show that when the refractive index of a photonic system is harmonically modulated, the phase of the modulation introduces an effective gauge potential for photons. This effective gauge potential can be used to create a photonic Aharonov-Bohm effect. We show that the photonic Aharonov-Bohm effect provides the optimal mechanism for achieving complete on-chip nonmagnetic optical isolation. PMID:22587255
Aharonov-Bohm Effect in Lattice Abelian Higgs Theory
Chernodub, M. N.; Gubarev, F. V.; Polikarpov, M.I.
1997-01-01
We study a field-theoretical analogue of the Aharonov-Bohm effect in two-, three- and four-dimensional Abelian Higgs models; the corresponding topological interaction is proportional to the linking number of the Abrikosov vortex and the particle world trajectories. We show that the Aharonov-Bohm effect gives rise to a nontrivial interaction of charged test particles. The numerical calculations in the three-dimensional model confirm this fact.
Aharonov-Bohm effect in a Class of Noncommutative Theories
Das, A.(University of Arizona, Tucson, AZ, 85721, USA); Falomir, H.; Gamboa, J.; Mendez, F.; Nieto, M.
2011-01-01
The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $\\theta$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schr\\"odinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of $...
Aharonov-Bohm effect in a class of noncommutative theories
Das, Ashok; Falomir, H.; Nieto, M.; Gamboa, J.; Méndez, F.
2011-08-01
The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in θ, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schrödinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of θ.
Aharonov-Bohm effect in a Class of Noncommutative Theories
Das, A; Gamboa, J; Mendez, F; Nieto, M
2011-01-01
The Aharonov-Bohm effect including spin-noncommutative effects is considered. At linear order in $\\theta$, the magnetic field is gauge invariant although spatially strongly anisotropic. Despite this anisotropy, the Schr\\"odinger-Pauli equation is separable through successive unitary transformations and the exact solution is found. The scattering amplitude is calculated and compared with the usual case. In the noncommutative Aharonov-Bohm case the differential cross section is independent of $\\theta$.
Gravitational Aharonov-Bohm effect in graphene
Full text. We would like to suggest that the Einstein theory of gravitation in 2+1 dimensions can be seen and even tested experimentally in possible realizable condensed matter materials, such as graphene. Deforming a graphene sheet in a conical surface this system makes possible the experimental study of relativistic massless quasiparticles with charge e on a two-dimensional, or equivalently, in the 'gravitational field (deficit angle) of a 'pointlike particle' of mass M (cone tip). This surface is locally flat. Then we study a kind of gravitational Aharonov-Bohm effect in a graphene sheet with a wedge removed and edges identified, i.e., a graphitic cone. The angular defect gives rise to a mismatch of the components of the graphene's relativistic charged quasiparticle wavefunctions (spinors) upon closed parallel transport around the (singular) cone tip. Such an affect should affect the basic electronic properties in 'conical graphene' as compared with their planar counterpart and it could be, in principle, detected experimentally. It is similar to the usual Aharonov-Bohm effect in electromagnetism, but simulated as a gravitational field by a deficit angle incorporated in the material. In principle, the effect proposed here could be detected by interference experiments in structured materials by measurements of the electronic transport in these graphitic materials and their relationships with the changes calculated in the quasiparticle wavefunctions. Therefore it could make available interesting probes to the Einstein theory of general relativity in two spatial dimensions. Then we propose a way of verifying, in a microscopic scale, some predictions of a theory that is usual. (author)
Aharonov-Casher and scalar Aharonov-Bohm topological effects.
Dulat, Sayipjamal; Ma, Kai
2012-02-17
We reexamine the topological and nonlocal natures of the Aharonov-Casher and scalar Aharonov-Bohm phase effects. The underlying U(1) gauge structure is exhibited explicitly. And the conditions for developing topological Aharonov-Casher and scalar Aharonov-Bohm phases are clarified. We analyze the arguments of M. Peshkin and H. J. Lipkin [Phys. Rev. Lett. 74, 2847 (1995)] in detail and show that they are based on the wrong Hamiltonian which yields their conclusion incorrect. PMID:22401183
The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics
Li, Kang; Dulat, Sayipjamal
2005-01-01
The Aharonov-Bohm (AB) effect in non-commutative quantum mechanics (NCQM) is studied. First, by introducing a shift for the magnetic vector potential we give the Schr$\\ddot{o}$dinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then by solving the Schr$\\ddot{o}$dinger equations, we obtain the Aharonov-Bohm (AB) phase on NC space and NC phase space, respectively.
Classical Electrodynamics without Fields and the Aharonov-Bohm effect
Stefanovich, Eugene V.
2008-01-01
The Darwin-Breit Hamiltonian is applied to the Aharonov-Bohm experiment. In agreement with the standard Maxwell-Lorentz theory, the force acting on electrons from infinite solenoids or ferromagnetic rods vanishes. However, the interaction energies and phase factors of the electron wave packets are non-zero. This allows us to explain the Aharonov-Bohm effect without involvement of electromagnetic potentials, fields, and topological properties of space.
Aharonov-Bohm Effect and Hidden Photons
Arias, Paola
2013-01-01
Signs of hypothetical light gauge bosons from a hidden sector may appear in Aharonov-Bohm-like experiments. The absence of signal in carried on experiments allow us to set a modest constraint to the mass and coupling constant of these particles. Our findings open the possibility to exploit the leaking of hidden magnetic field in a different setup of experiments.
Global analogue of the Aharonov-Bohm effect
This thesis deals with a global analogue of the Aharonov-Bohm effect previously pointed out by other authors. The effect was not well understood because the pure Aharonov-Bohm cross section was thought to be merely an approximate low energy limit. This thesis provides a detailed analysis and reveals that in the particular model considered, there is an exact Aharonov-Bohm cross section over the energy range that a mass splitting occurs. At energies slightly above the mass splitting, the effect has completely disappeared and there is effectively no scattering at large distances. This is a curious observation as it was previously thought that a global theory would not act exactly like a local one over an extended range of energies. It begs the heretical speculation that experimentally observed forces modelled with Lagrangians possessing local symmetries may have an underlying global theory
The covariant, time-dependent Aharonov-Bohm Effect
Singleton, Douglas
2013-01-01
We discuss two possible covariant generalizations of the Aharonov-Bohm effect - one expression in terms of the space-time line integral of the four-vector potential and the other expression in terms of the space-time "area" integral of the electric and magnetic fields written in terms of the Faraday 2-form. These expressions allow one to calculate the Aharonov-Bohm effect for time-dependent situations. In particular, we use these expressions to study the case of an infinite solenoid with a time varying flux and find that the phase shift is zero due to a cancellation of the Aharonov-Bohm phase shift with a phase shift coming from the Lorentz force associated with the electric field, ${\\bf E} = - \\partial_t {\\bf A}$, outside the solenoid. This result may already have been confirmed experimentally.
Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids
Furtado, Claudio; Carvalho, A. M. de M.; de Andrade, L. C. Garcia; Moraes, F.
2004-01-01
In this article we discuss the analogy between superfluids and a spinning thick cosmic string. We use the geometrical approach to obtain the geometrical phases for a phonon in the presence of a vortex. We use loop variables for a geometric description of Aharonov-Bohm effect in these systems. We use holonomy transformations to characterize globally the "space-time" of a vortex and in this point of view we study the gravitational analog of the Aharonov-Bohm effect in this system. We demonstrat...
Aharonov-Bohm effect in many-electron quantum rings
Kotimaki, V.; Rasanen, E.
2010-01-01
The Aharonov-Bohm effect is investigated in two-dimensional, single-terminal quantum rings in magnetic fields by using time-dependent density-functional theory. We find multiple transport loops leading to the oscillation periods of h/(en), where n is the number of loops. We show that the Aharonov-Bohm oscillations are relatively weakly affected by the electron-electron interactions, whereas the ring width has a strong effect on the characteristics of the oscillations. Our results propose that...
Effect of Aharonov-Bohm Phase on Spin Tunneling
Park, ChangSoo; Park, D. K.
1999-01-01
The role of Aharonov-Bohm effect in quantum tunneling is examined when a potential is defined on the $S^1$ and has $N$-fold symmetry. We show that the low-lying energy levels split from the $N$-fold degenerate ground state oscillate as a function of the Aharonov-Bohm phase, from which general degeneracy conditions depending on the magnetic flux is obtained. We apply these results to the spin tunneling in a spin system with $N$-fold rotational symmetry around a hard axis.
Relativistic Aharonov--Bohm effect in the presence of two-dimensional Coulomb potential
Khalilov, Vladislav
2004-01-01
We obtain exact solutions to the Dirac equation and the relevant binding energies in the combined Aharonov--Bohm--Coulomb potential in 2+1 dimensions. By means of solutions obtained the quantum Aharonov--Bohm effect is studied for free and bound electron states. We show that the total scattering amplitude in the combined Aharonov--Bohm--Coulomb potential is a sum of the Aharonov--Bohm and the Coulomb scattering amplitudes. This modifies expression for the standard Aharonov--Bohm cross section...
Magnus Force and Aharonov-Bohm Effect in Superfluids
Sonin, E. B.
2001-01-01
The paper addresses the problem of the transverse force (Magnus force) on a vortex in a Galilean invariant quantum Bose liquid. Interaction of quasiparticles (phonons) with a vortex produces an additional transverse force (Iordanskii force). The Iordanskii force is related to the acoustic Aharonov--Bohm effect.Connection of the effective Magnus force with the Berry phase is also discussed.
Non-traditional Aharonov-Bohm effects in condensed matter
In 1959, Aharonov and Bohm proposed an elegant experiment demonstrating observability of electromagnetic potentials (or, which is the same, the non-locality of the wave function of charged particles) in quantum mechanics. This paper discusses the Aharonov-Bohm effect, based on the fundamental principles of quantum theory, as the superposition principles, the quantum character of motion of particles and locality of the interaction of a charge with an electromagnetic potential Lint = jμAμ. It is thus no wonder that the Aharonov-Bohm's paper aroused much dispute which is still ongoing. Originally, the Aharonov-Bohm effect (ABE) means the dependence of the interference pattern on the magnetic fluid flux φ in a Gendaken experiment on a coherent electron beam in the field of an infinitely thin solenoid. Later, however, it became common to refer to the Aharonov-Bohm phenomenon wherever the characteristics of systems under study appear to depend on the flux φ in the absence of electric and magnetic fields. In this sense, it was highly interesting to analyze the ABE in condensed media (the many-particle Aharonov-Bohm effect), in particular to study the dependence of the thermodynamic and kinetic characteristics, e.g., of metal on the flux. Such a problem was first discussed by Byers and Yang who formulated the general theorems related to the ABE in conducting condensed media. The next important step was the work of Kulik who formulated a concrete model and calculated the flux-dependent contribution to the metal free energy and provided a first clear formulation of the requirements to reveal
Exner, Pavel; Stovicek, Pavel; Vytras, Petr
2001-01-01
The most general admissible boundary conditions are derived for an idealised Aharonov-Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; other two parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic field. The generalised boundary conditions may be regarded as a combination of the Aharonov-Bohm effect with a poi...
Observation of Aharonov-Bohm effects by neutron interferometry
The special and unique techniques of neutron interferometry have been used to observe a number of topological effects. These include the quantum mechanical phase shift of a neutron due to the Earth's rotation (the quantum analog of the Michelson-Gale-Pearson experiment with light), the phase shift of a particle carrying a magnetic moment (a neutron) encircling a line charge (the Aharonov-Casher effect) and the scalar Aharonov-Bohm effect, observed with a pulsed magnetic field solenoid and time-of-flight neutron detection. On the occasion of the 50th anniversary of the Aharonov-Bohm paper, we provide an overview of the neutron interferometry technique and a description of these three historic experiments.
Aharonov-Bohm effect induced by circularly polarized light
Sigurdsson, H.; Kibis, O. V.; Shelykh, I. A.
2015-11-01
We demonstrated theoretically that the strong electron interaction with circularly polarized photons in ring-like nanostructures changes the phase of electron wave. This optically-induced effect is caused by the breaking of time-reversal symmetry and is similar to the Aharonov-Bohm effect. As a consequence of this phenomenon, the conductance of mesoscopic rings irradiated by a circularly polarized electromagnetic wave behaves as an oscillating function of the intensity and frequency of the wave.
Scalar Aharonov-Bohm effect with longitudinally polarized neutrons
In the scalar Aharonov-Bohm effect, a charged particle (electron) interacts with the scalar electrostatic potential U in the field-free (i.e., force-free) region inside an electrostatic cylinder (Faraday cage). Using a perfect single-crystal neutron interferometer we have performed a ''dual'' scalar Aharonov-Bohm experiment by subjecting polarized thermal neutrons to a pulsed magnetic field. The pulsed magnetic field was spatially uniform, precluding any force on the neutrons. Aligning the direction of the pulsed magnetic field to the neutron magnetic moment also rules out any classical torque acting to change the neutron polarization. The observed phase shift is purely quantum mechanical in origin. A detailed description of the experiment, performed at the University of Missouri Research Reactor, and its interpretation is given in this paper. (c) 1999 The American Physical Society
Spin- and localization-induced fractional Aharonov-Bohm effect
Emperador, A.; Pederiva, F.; Lipparini, E.
2003-09-01
We performed a theoretical analysis of the Aharonov-Bohm oscillations of the ground-state energy of quasi-one-dimensional quantum rings in a magnetic field, recently observed in conductance experiments, by means of quantum Monte Carlo calculations. The model rings considered contain N=10 and N=4 electrons, with radii of 20 and 120 nm, respectively. These parameters give a close description of the nanorings analyzed in the experiments. In particular, the two cases well reproduce the high- and low-electron-density regimes. For N=10, we have found fractional Aharonov-Bohm effect with a period Φ0/2 due to the changes in the total spin of the ground state. For N=4, we have found fractional oscillations with a period Φ0/4, which are shown to be a consequence of strong localization.
Aharonov-Bohm Effect in Cyclotron and Synchrotron Radiations
Bagrov, V G; Levin, A; Tlyachev, V B
2000-01-01
We study the impact of Aharonov-Bohm solenoid on the radiation of a charged particle moving in a constant uniform magnetic field. With this aim in view, exact solutions of Klein-Gordon and Dirac equations are found in the magnetic-solenoid field. Using such solutions, we calculate exactly all the characteristics of one-photon spontaneous radiation both for spinless and spinning particle. Considering non-relativistic and relativistic approximations, we analyze cyclotron and synchrotron radiations in detail. Radiation peculiarities caused by the presence of the solenoid may be considered as a manifestation of Aharonov-Bohm effect in the radiation. In particular, it is shown that new spectral lines appear in the radiation spectrum. Due to angular distribution peculiarities of the radiation intensity, these lines can in principle be isolated from basic cyclotron and synchrotron radiation spectra
Noncommutative analogue Aharonov-Bohm effect and superresonance
M.A. Anacleto; Brito, F. A.; E. Passos
2012-01-01
We consider the idea of modeling a rotating acoustic black hole by an idealized draining bathtub vortex which is a planar circulating flow phenomenon with a sink at the origin. We find the acoustic metric for this phenomenon from a noncommutative Abelian Higgs model. As such the acoustic metric not only describes a rotating acoustic black hole but also inherits the noncommutative characteristic of the spacetime. We address the issues of superresonance and analogue Aharonov-Bohm (AB) effect in...
The Fano Effect in Aharonov-Bohm interferometers
Entin-Wohlman, O.; Aharony, A.; Imry, Y.; Levinson, Y.
2001-01-01
After briefly reviewing the Fano effect, we explain why it may be relevant to various types of Aharonov-Bohm interferometers. We discuss both closed (electron conserving) and open interferometers, in which one path contains either a simple quantum dot or a decorated quantum dot (with more than one internal state or a parallel path). The possible relevance to some hitherto unexplained experimental features is also discussed.
Aharonov-Bohm effect of excitons in nanorings
Hu, Hui; Zhu, Jia-Lin; Li, Dai-Jun; Xiong, Jia-Jiong
2001-05-01
The magnetic field effects on excitons in an InAs nanoring are studied theoretically. By numerically diagonalizing the effective-mass Hamiltonian of the problem that can be separated into terms in center-of-mass and relative coordinates, we calculate the low-lying excitonic energy levels and oscillator strengths as a function of the ring width and the strength of an external magnetic field. It is shown that in the presence of Coulomb correlation, the so-called Aharonov-Bohm effect of excitons exists in a finite (but small) width nanoring. However, when the ring width becomes large, the non-simply-connected geometry of nanorings is destroyed, causing the suppression of the Aharonov-Bohm effect. The analytical results are obtained for a narrow-width nanoring in which the radial motion is the fastest one and adiabatically decoupled from the azimuthal motions. The conditional probability distribution calculated for the low-lying excitonic states allows identification of the presence of the Aharonov-Bohm effect. The linear optical susceptibility is also calculated as a function of the magnetic field, to be compared with the future measurements of optical emission experiments on InAs nanorings.
Aharonov-Bohm effect in optical activity
Optically active media have the helical and dissymmetric crystal structure, which constrains the motions of the electrons to a helical path under the influence of the incident electric field. The charge flow along the helices induces a magnetic field in the direction of the axis of helices. The helical structure hence acts as natural micro-solenoids for the electromagnetic waves passing through them. Optical rotation is related to the difference in the accumulative Aharonov-Bohm (AB) phase between the right- and the left-circularly polarized waves. The AB phase is proportional to the angular momentum of an electron moving around the micro-solenoid. Originally the AB phase is shown to be a continuous function of the magnetic flux. However, quantization of the geometrical angular momentum leads to the quantized AB phase. The rotatory power and the Verdet constant are proportional to the refractive index of the medium. The quantized current in the micro-solenoid is proportional to the Bohr magneton and inversely proportional to the area of the helices.
On the Aharonov-Bohm Effect and Why Heisenberg Captures Nonlocality Better Than Schr\\"odinger
Aharonov, Yakir
2013-01-01
I discuss in detail the history of the Aharonov-Bohm effect in Bristol and my encounters with Akira Tonomura later on. I then propose an idea that developed following the publication of the Aharonov-Bohm effect, namely the importance of modulo momentum and Heisenberg representation in dealing with non-local quantum phenomena.
On the Locality Principle Keeping in Aharonov-Bohm Effect
Gritsunov, Alexander
2013-01-01
The locality principle fulfillment in the Aharonov-Bohm (AB) effect is analyzed from the point of view of a self-sufficient potential formalism based on so-called gradient hypothesis in electrodynamics. The "magnetic" kind of AB effect is examined (as the quantum charged particle moves to an infinitely long solenoid with a permanent current), and no locality principle violation recognized if the gradient hypothesis is used. A conclusion is made that AB effect is no longer a physical and electrodynamic "paradox".
The Early History of the Aharonov-Bohm Effect
Hiley, B J
2013-01-01
This paper traces the early history of the Aharonov-Bohm effect. It appears to have been `discovered' at least three times to my knowledge before the defining paper of Aharonov and Bohm appeared in 1959. The first hint of the effect appears in Germany in 1939, immediately disappearing from sight in those troubled times. It reappeared in a paper in 1949, ten years before the defining paper appeared. Here I report the background to the early evolution of this effect, presenting first hand unpublished accounts reported to me by colleagues at Birkbeck College in the University of London.
Analogue Aharonov-Bohm effect in neo-Newtonian theory
Anacleto, M A; Brito, F A; Passos, E
2015-01-01
We address the issues of the scattering of massless planar scalar waves by an acoustic black hole in neo-Newtonian hydrodynamics. We then compute the differential cross section through the use of the partial wave approach in the neo-Newtonian theory which is a modification of the usual Newtonian theory that correctly incorporates the effects of pressure. We mainly show that the scattering of planar waves leads to a modified analogue Aharonov-Bohm effect due to a nontrivial response of the parameters defining the equation of state.
Spectroscopic detectability of the molecular Aharonov-Bohm effect
Englman, R.
2016-01-01
It is theoretically shown that the emission spectra from an excited Jahn-Teller state in which the ions undergo a forced periodic trajectory have an M-shaped form, directly due to the sign change by the Berry-phase factor. The presence of a weak spectral sideline is noted and the effects of a nonlinear vibronic coupling are calculated. Experimental verifications of the results, e.g., on R'-centers in LiF, are proposed. The dip in the M-shaped emission line is a novel, and perhaps unique, spectroscopic manifestation of the "molecular Aharonov-Bohm effect."
Analogue Aharonov-Bohm effect in neo-Newtonian theory
Anacleto, M. A.; Salako, I. G.; Brito, F. A.; Passos, E.
2015-12-01
We address the issues of the scattering of massless planar scalar waves by an acoustic black hole in neo-Newtonian hydrodynamics. We then compute the differential cross section through the use of the partial wave approach in the neo-Newtonian theory which is a modification of the usual Newtonian theory that correctly incorporates the effects of pressure. We mainly show that the scattering of planar waves leads to a modified analogue Aharonov-Bohm effect due to a nontrivial response of the parameters defining the equation of state.
Analogue Aharonov-Bohm effect in neo-Newtonian theory
Anacleto, M.A.(Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraíba, Brazil); Salako, I. G.; Brito, F. A.; Passos, E.
2015-01-01
We address the issues of the scattering of massless planar scalar waves by an acoustic black hole in neo-Newtonian hydrodynamics. We then compute the differential cross section through the use of the partial wave approach in the neo-Newtonian theory which is a modification of the usual Newtonian theory that correctly incorporates the effects of pressure. We mainly show that the scattering of planar waves leads to a modified analogue Aharonov-Bohm effect due to a nontrivial response of the par...
Paradoxes of the Aharonov-Bohm and the Aharonov-Casher effects
Vaidman, Lev
2013-01-01
For a believer in locality of Nature, the Aharonov-Bohm effect and the Aharonov-Casher effect are paradoxes. I discuss these and other Aharonov's paradoxes and propose a local explanation of these effects. If the solenoid in the Aharonov-Bohm effect is treated quantum mechanically, the effect can be explained via local interaction between the field of the electron and the solenoid. I argue that the core of the Aharonov-Bohm and the Aharonov-Casher effects is that of quantum entanglement: the ...
Kirchhoff diffraction optics and the nascent Aharonov-Bohm effect: a theorem
Textbook diffraction optics, Kirchhoff diffraction, is connected to the Aharonov-Bohm effect of quantum mechanics by an easy theorem proved here. The connection is between the Kirchhoff wave field and the Aharonov-Bohm quantum wave field in the limit of zero flux: the 'nascent' Aharonov-Bohm effect. The diffracting opaque screen of Kirchhoff optics is replaced in the quantum mechanics by a magnetic flux line, or loop, in the shape of the boundary edge of the screen. The gauge must be chosen appropriately: a delta function on that surface, spanning the boundary edge, which matches the screen.
Gravito-electromagnetic Aharonov-Bohm effect: some rotation effects revised
Ruggiero, Matteo Luca
2010-01-01
By means of the description of the standard relative dynamics in terms of gravito-electromagnetic fields, in the context of natural splitting, we formally introduce the gravito-magnetic Aharonov-Bohm effect. Then, we interpret the Sagnac effect as a gravito-magnetic Aharonov-Bohm effect and we exploit this formalism for studying the General Relativistic corrections to the Sagnac effect in stationary and axially symmetric geometries.
What did we learn from the Aharonov-Bohm effect? Is spin 1/2 different?
I review what has been learned about fundamental issues in quantum mechanics from the Aharonov-Bohm effect. Following that, I consider the Aharonov-Casher effect and the Scalar Aharonov-Bohm effect, in both of which a spin-1/2 particle interacts with a local electromagnetic field through its magnetic moment, and conclude that those effects can be described as observable effects of local torques
The bound state Aharonov-Bohm effect around a cosmic string revisited
Filgueiras, C.; Moraes, Fernando
2005-01-01
In this article we observe that the self-adjoint extension of the Hamiltonian of a particle moving around a shielded cosmic string gives rise to a gravitational analogue of the bound state Aharonov-Bohm effect.
Gauge equivalence classes of flat connections in the Aharonov-Bohm effect
M.A. Aguilar; Isidro, J. M.; Socolovsky, M.
2003-01-01
In this note we present a simplified derivation of the fact that the moduli space of flat connections in the abelian Aharonov-Bohm effect is isomorphic to the circle. The length of this circle is the electric charge.
Revisiting the Marton, Simpson, and Suddeth experimental confirmation of the Aharonov-Bohm effect
Macdougall, James; Singleton, Douglas; Vagenas, Elias C.
2015-09-01
We perform an "archeological" study of one of the original experiments used as evidence for the static, time-independent Aharonov-Bohm effect. Since the experiment in question [1] involved a time varying magnetic field we show that there are problems with the explanation of this experiment as a confirmation of the static Aharonov-Bohm effect - specifically the previous analysis ignored the electric field which arises in conjunction with a time-varying magnetic flux. We further argue that the results of this experiment do in fact conform exactly to the recent prediction [2,3] of a cancellation between the magnetic and electric phase shifts for the time-dependent Aharonov-Bohm effect. To resolve this issue a new time-dependent Aharonov-Bohm experiment is called for.
Path integrals with topological constraints: Aharonov-Bohm effect and polymer entanglements
Wiegel, F.W.
1981-01-01
For Wiener- and Feynman integrals over paths with certain topological properties we compare various methods for explicit calculation. This leads to a one-to-one correspondence between the Aharonov-Bohm effect and a certain polymer entanglement problem. We briefly comment on two generalizations of the Aharonov-Bohm effect. First, we consider this effect due to a closed magnetic flux loop of arbitrary shape; next, we consider the combined effect due to a gas of microscopic magnetic flux loops.
Photon mass and quantum effects of the Aharonov-Bohm type
Spavieri, G.; M. Rodriguez
2007-01-01
The magnetic field due to the photon rest mass $m_{ph}$ modifies the standard results of the Aharonov-Bohm effect for electrons, and of other recent quantum effects. For the effect involving a coherent superposition of beams of particles with opposite electromagnetic properties, by means of a table-top experiment, the limit $m_{ph}x10^{-51}g$ is achievable, improving by 6 orders of magnitude that derived by Boulware and Deser for the Aharonov-Bohm effect.
Noncommutative analogue Aharonov-Bohm effect and superresonance
Anacleto, M A; Passos, E
2012-01-01
We consider the idea of modeling a rotating acoustic black hole by an idealized draining bathtub vortex which is a planar circulating flow phenomenon with a sink at the origin. We find the acoustic metric for this phenomenon from a noncommutative Abelian Higgs model. As such the acoustic metric not only describes a rotating acoustic black hole but also inherits the noncommutative characteristic of the spacetime. We address the issues of superresonance and analogue Aharonov-Bohm (AB) effect in this background. We mainly show that the scattering of planar waves by a draining bathtub vortex leads to a modified AB effect and due to spacetime noncommutativity, the phase shift persists even in the limit where the parameters associated with the circulation and draining vanish. Finally, we also find that the analogue AB effect and superresonance are competing phenomena at a noncommutative spacetime.
Noncommutative analogue Aharonov-Bohm effect and superresonance
Anacleto, M. A.; Brito, F. A.; Passos, E.
2013-06-01
We consider the idea of modeling a rotating acoustic black hole by an idealized draining bathtub vortex which is a planar circulating flow phenomenon with a sink at the origin. We find the acoustic metric for this phenomenon from a noncommutative Abelian Higgs model. As such the acoustic metric not only describes a rotating acoustic black hole but also inherits the noncommutative characteristic of the spacetime. We address the issues of superresonance and analogue Aharonov-Bohm (AB) effect in this background. We mainly show that the scattering of planar waves by a draining bathtub vortex leads to a modified AB effect and due to spacetime noncommutativity, the phase shift persists even in the limit where the parameters associated with the circulation and draining vanish. Finally, we also find that the analogue AB effect and superresonance are competing phenomena at a noncommutative spacetime.
The Aharonov-Bohm and Aharonov-Casher effects and electromagnetic angular momentum
A semiclassical explanation for the Aharonov-Bohm and Aharonov-Casher effects is presented. It is shown that these quantum-mechanical effects derive from nontrivial electromagnetic angular momentum inherent to a system containing both charges and magnetic dipoles. It is emphasized that a unified description of the Aharonov-Bohm effect with a solenoid of general shape, both open and closed, is developed in terms of the electromagnetic angular momentum carried by the flux lines that constitute real magnetic flux. (orig.)
Non-Abelian Vortices with an Aharonov-Bohm Effect
Evslin, Jarah; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2014-01-01
The interplay of gauge dynamics and flavor symmetries often leads to remarkably subtle phenomena in the presence of soliton configurations. Non-Abelian vortices -- vortex solutions with continuous internal orientational moduli -- provide an example. Here we study the effect of weakly gauging a U(1)_R subgroup of the flavor symmetry on such BPS vortex solutions. Our prototypical setting consists of an SU(2) x U(1) gauge theory with N_f=2 sets of fundamental scalars that break the gauge symmetry to an "electromagnetic" U(1). The weak U(1)_R gauging converts the well-known CP1 orientation modulus |B| of the non-Abelian vortex into a parameter characterizing the strength of the magnetic field that is responsible for the Aharonov-Bohm effect. As the phase of B remains a genuine zero mode while the electromagnetic gauge symmetry is Higgsed in the interior of the vortex, these solutions are superconducting strings.
Thermoelectric effects in a rectangular Aharonov-Bohm geometry
Pye, A. J.; Faux, D. A.; Kearney, M. J.
2016-04-01
The thermoelectric transport properties of a rectangular Aharonov-Bohm ring at low temperature are investigated using a theoretical approach based on Green's functions. The oscillations in the transmission coefficient as the field is varied can be used to tune the thermoelectric response of the ring. Large magnitude thermopowers are obtainable which, in conjunction with low conductance, can result in a high thermoelectric figure of merit. The effects of single site impurities and more general Anderson disorder are considered explicitly in the context of evaluating their effect on the Fano-type resonances in the transmission coefficient. Importantly, it is shown that even for moderate levels of disorder, the thermoelectric figure of merit can remain significant, increasing the appeal of such structures from the perspective of specialist thermoelectric applications.
Two-particle Aharonov-Bohm effect and Entanglement in the electronic Hanbury Brown Twiss setup
Samuelsson, Martin Peter; Sukhorukov, Eugene; Buttiker, Markus
2003-01-01
We analyze a Hanbury Brown-Twiss geometry in which particles are injected from two independent sources into a mesoscopic conductor in the quantum Hall regime. All partial waves end in different reservoirs without generating any single-particle interference; in particular, there is no single-particle Aharonov-Bohm effect. However, exchange effects lead to two-particle Aharonov-Bohm oscillations in the zero-frequency current cross correlations. We demonstrate that this is related to two-particl...
Aharonov-Bohm Effect in Perturbation Theory.
Purcell, Kay M.; Henneberger, Walter C.
1978-01-01
The Aharonov-Bohn effect is obtained in first-order perturbation theory. It is shown that the effect occurs only when the initial state is a superposition of eigenstates of Lz corresponding to eigenvalues having opposite sign. (Author/GA)
Magnetic Catalysis of Dynamical Symmetry Breaking and Aharonov-Bohm Effect
Miransky, V.A.
1998-01-01
The phenomenon of the magnetic catalysis of dynamical symmetry breaking is based on the dimensional reduction $D\\to D-2$ in the dynamics of fermion pairing in a magnetic field. We discuss similarities between this phenomenon and the Aharonov-Bohm effect. This leads to the interpretation of the dynamics of the (1+1)-dimensional Gross-Neveu model with a non-integer number of fermion colors as a quantum field theoretical analogue of the Aharonov-Bohm dynamics.
The Aharonov-Casher and scalar Aharonov-Bohm topological effects
Dulat, Sayipjamal; Ma, Kai
2012-01-01
We reexamine the topological and nonlocal natures of the Aharonov-Casher and scalar Aharonov-Bohm phase effects. The underlying U(1) gauge structure is exhibited explicitly. And the conditions for developing topological Aharonov-Casher and scalar Aharonov-Bohm phases are clarified. We analyse the arguments of M. Peshkin and H. J. Lipkin (Phys. Rev. Lett. 74, 2847(1995)) in detail and show that they are based on the wrong Hamiltonian which yields their conclusion incorrect.
Whirling Waves and the Aharonov-Bohm Effect for Relativistic Spinning Particles
Girotti, H. O.; Romero, F. Fonseca
1996-01-01
The formulation of Berry for the Aharonov-Bohm effect is generalized to the relativistic regime. Then, the problem of finding the self-adjoint extensions of the (2+1)-dimensional Dirac Hamiltonian, in an Aharonov-Bohm background potential, is solved in a novel way. The same treatment also solves the problem of finding the self-adjoint extensions of the Dirac Hamiltonian in a background Aharonov-Casher.
Time-dependent Aharonov-Bohm effect on the noncommutative space
Ma, Kai; Wang, Jian-Hua; Yang, Huan-Xiong
2016-08-01
We study the time-dependent Aharonov-Bohm effect on the noncommutative space. Because there is no net Aharonov-Bohm phase shift in the time-dependent case on the commutative space, therefore, a tiny deviation from zero indicates new physics. Based on the Seiberg-Witten map we obtain the gauge invariant and Lorentz covariant Aharonov-Bohm phase shift in general case on noncommutative space. We find there are two kinds of contribution: momentum-dependent and momentum-independent corrections. For the momentum-dependent correction, there is a cancellation between the magnetic and electric phase shifts, just like the case on the commutative space. However, there is a non-trivial contribution in the momentum-independent correction. This is true for both the time-independent and time-dependent Aharonov-Bohm effects on the noncommutative space. However, for the time-dependent Aharonov-Bohm effect, there is no overwhelming background which exists in the time-independent Aharonov-Bohm effect on both commutative and noncommutative space. Therefore, the time-dependent Aharonov-Bohm can be sensitive to the spatial noncommutativity. The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter θ, and through the surface enclosed by the trajectory of charged particle. More interestingly, there is an anti-collinear relation between the logarithms of the magnetic field B and the averaged flux Φ / N (N is the number of fringes shifted). This nontrivial relation can also provide a way to test the spatial noncommutativity. For BΦ / N ∼ 1, our estimation on the experimental sensitivity shows that it can reach the 10 GeV scale. This sensitivity can be enhanced by using stronger magnetic field strength, larger magnetic flux, as well as higher experimental precision on the phase shift.
Non-Abelian vortices with an Aharonov-Bohm effect
Evslin, Jarah [TPCSF, IHEP, Chinese Academy of Sciences,Beijing (China); Theoretical physics division, IHEP, Chinese Academy of Sciences,Beijing (China); Konishi, Kenichi [Department of Physics “Enrico Fermi”, University of Pisa,Largo Pontecorvo 3, 56127, Pisa (Italy); INFN, Sezione di Pisa,Largo Pontecorvo 3, 56127, Pisa (Italy); Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University,4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521 (Japan); Ohashi, Keisuke [Department of Physics, Osaka City University,Osaka (Japan); Vinci, Walter [London Centre for Nanotechnology and Computer Science, University College London,17-19 Gordon Street, London, WC1H 0AH (United Kingdom)
2014-01-16
The interplay of gauge dynamics and flavor symmetries often leads to remarkably subtle phenomena in the presence of soliton configurations. Non-Abelian vortices — vortex solutions with continuous internal orientational moduli — provide an example. Here we study the effect of weakly gauging a U(1){sub R} subgroup of the flavor symmetry on such BPS vortex solutions. Our prototypical setting consists of an SU(2)×U(1) gauge theory with N{sub f}=2 sets of fundamental scalars that break the gauge symmetry to an “electromagnetic' U(1). The weak U(1){sub R} gauging converts the well-known CP{sup 1} orientation modulus |B| of the non-Abelian vortex into a parameter characterizing the strength of the magnetic field that is responsible for the Aharonov-Bohm effect. As the phase of B remains a genuine zero mode while the electromagnetic gauge symmetry is Higgsed in the interior of the vortex, these solutions are superconducting strings.
Analytical and Numerical Study of the Aharonov--Bohm Effect in 3D and 4D Abelian Higgs Model
Chernodub, M. N.; Gubarev, F. V.; Polikarpov, M.I.
1996-01-01
We discuss the Aharonov--Bohm effect in three and four dimensional non--compact lattice Abelian Higgs model. We show analytically that this effect leads to the long--range Coulomb interaction of the charged particles, which is confining in three dimensions. The Aharonov--Bohm effect is found in numerical calculations in 3D Abelian Higgs model.
Time-dependent Aharonov-Bohm effect on the noncommutative space
Ma, Kai; Yang, Huan-Xiong
2016-01-01
We study the time-dependent Aharonov-Bohm effect on the noncommutative space. Because there is no net Aharonov-Bohm phase shift in the time-dependent case on the commutative space, therefore tiny deviation from zero indicates new physics. Based on the Seiberg-Witten map we obtained the gauge invariant and Lorentz covariant Aharonov-Bohm phase shift on noncommutative space in general case. We find there are two kinds of contributions: momentum-dependent and momentum-independent corrections. For the momentum-dependent correction, there is a cancellation between the magnetic and electric phase shifts, just like the case on the commutative space. However, there is a non-trivial contribution in the momentum-independent correction. This is true for both the time-independent and time-dependent Aharonov-Bohm effects on the noncommutative space. However, for the time-dependent Aharonov-Bohm effect, there is no overwhelming background which exists on both commutative and noncommutative space for the time-independent Ah...
Internal frame dragging and a global analog of the Aharonov-Bohm effect
March-Russell, John(Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, U.K.); Preskill, John; Wilczek, Frank
1992-01-01
It is shown that the breakdown of a global symmetry group to a discrete subgroup can lead to analogs of the Aharonov-Bohm effect. At sufficiently low momentum transfer, the cross section for scattering of a particle with nontrivial Z2 charge off a global vortex is almost equal to (but definitely different from) maximal Aharonov-Bohm scattering; the effect goes away at large momentum transfer. The scattering of a spin-1/2 particle off a magnetic vortex provides an amusing experimentally realiz...
On the role of potentials in the Aharonov-Bohm effect
Vaidman, Lev
2011-01-01
There is a consensus today that the the main lesson of the Aharonov-Bohm effect is that a picture of electromagnetism based on the local action of the field strengths is not possible in quantum mechanics. Contrary to this statement it is argued here that when the source of the electromagnetic potential is treated in the framework of quantum theory, the Aharonov-Bohm effect can be explained without the notion of potentials. It is explained by local action of the field of the electron on the so...
The Crucial Role of Inert Source in the Magnetic Aharonov-Bohm Effect
Comay, E.
2009-01-01
The role of the inert magnetic source used in the Tonomura experiment that has confirmed the magnetic Aharonov-Bohm effect is discussed. For this purpose, an analysis of a thought experiment is carried out. Here the permanent magnet is replaced by a classical source which is made of an ideal coil. A detailed calculation of this noninert source proves that in this case the effect disappears. This outcome provides another support for the crucial role of an inert source in the Aharonov-Bohm effe...
Interference between the Aharonov-Bohm and Aharonov-Casher effects
After a discussion of the principles of the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects, the possibility of observing the interference between them is discussed. The implications of the AB and AC effects for anyon physics are also considered. (author) 8 refs., 3 figs
Duality in the Aharonov-Casher and Aharonov-Bohm effects
A neutral particle with a magnetic moment interacts with a charged particle. Such an interaction is invariant under the interchange of the particles. This interchangeability or duality of the particles elucidates subtleties of the Aharonov-Bohm and Aharonov-Casher effects, including whether and how these two effects are themselves dual.
Gravitational Aharonov-Bohm effect due to noncommutative BTZ black hole
Anacleto, M A; Passos, E
2014-01-01
In this paper we consider the scattering of massless planar scalar waves by a noncommutative BTZ black hole. We compute the differential cross section via the partial wave approach, and we mainly show that the scattering of planar waves leads to a modified Aharonov-Bohm effect due to spacetime noncommutativity
Gravitational Aharonov-Bohm effect due to noncommutative BTZ black hole
Anacleto, M. A.; Brito, F. A.; Passos, E.
2015-04-01
In this paper we consider the scattering of massless planar scalar waves by a noncommutative BTZ black hole. We compute the differential cross section via the partial wave approach, and we mainly show that the scattering of planar waves leads to a modified Aharonov-Bohm effect due to spacetime noncommutativity.
The bound-state Aharonov-Bohm effect around a cosmic string revisited
In this Letter we observe that the self-adjoint extension of the Hamiltonian of a particle moving around a cosmic string gives rise to a gravitational analogue of the bound-state Aharonov-Bohm effect without the need of confining walls
Revisiting the Marton, Simpson, and Suddeth experimental confirmation of the Aharonov-Bohm effect
Macdougall, James; Vagenas, Elias C
2015-01-01
We perform an "archeological" study of one of the original experiments used as evidence for the static, time-independent Aharonov-Bohm effect. Since the experiment in question [L. Marton, J. A. Simpson, and J. A. Suddeth, Rev. Sci. Instr. 25, 1099 (1954)] involved a time varying magnetic field we show that there are problems with the explanation of this experiment as a confirmation of the static Aharonov-Bohm effect -- specifically the previous analysis ignored the electric field which arises in conjunction with a time-varying magnetic flux. We further argue that the results of this experiment do in fact conform exactly to the recent prediction [D. Singleton and E. Vagenas, Phys. Lett. B723, 241 (2013); J. MacDougall and D. Singleton, J. Math. Phys. 55, 042101 (2014)] of a cancellation between the magnetic and electric phase shifts for the time-dependent Aharonov-Bohm effect. To resolve this issue a new time-dependent Aharonov-Bohm experiment is called for.
Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect
Macdougall, James
2013-01-01
Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect -- the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology of the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.
Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect
Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology of the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed
Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect
Macdougall, James, E-mail: jbm34@mail.fresnostate.edu; Singleton, Douglas, E-mail: dougs@csufresno.edu [Department of Physics, California State University Fresno, Fresno, California 93740-8031 (United States)
2014-04-15
Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology of the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.
Eckle, H. -P.; Johannesson, H; Stafford, C. A.
2000-01-01
We study the persistent currents induced by both the Aharonov-Bohm and Aharonov-Casher effects in a one-dimensional mesoscopic ring coupled to a side-branch quantum dot at Kondo resonance. For privileged values of the Aharonov-Bohm-Casher fluxes, the problem can be mapped onto an integrable model, exactly solvable by a Bethe ansatz. In the case of a pure magnetic Aharonov-Bohm flux, we find that the presence of the quantum dot has no effect on the persistent current. In contrast, the Kondo re...
Dispersionless forces and the Aharonov-Bohm effect
Batelaan, H.; Becker, M.
2015-11-01
The independence of the Aharonov-Bohm phase shift on particle velocity is one of its defining properties. The classical counterpart to this dispersionless behavior is the absence of forces along the direction of motion of the particle. A reevaluation of the experimental demonstration that forces are absent in the AB physical system is given, including previously unpublished data. It is shown that the debate on the presence or absence of forces is not settled. Experiments that measure the influence of magnetic permeability on forces and search for dispersionless quantum forces are proposed.
The Aharonov-Bohm effect and Tonomura et al. experiments: Rigorous results
The Aharonov-Bohm effect is a fundamental issue in physics. It describes the physically important electromagnetic quantities in quantum mechanics. Its experimental verification constitutes a test of the theory of quantum mechanics itself. The remarkable experiments of Tonomura et al. ['Observation of Aharonov-Bohm effect by electron holography', Phys. Rev. Lett 48, 1443 (1982) and 'Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave', Phys. Rev. Lett 56, 792 (1986)] are widely considered as the only experimental evidence of the physical existence of the Aharonov-Bohm effect. Here we give the first rigorous proof that the classical ansatz of Aharonov and Bohm of 1959 ['Significance of electromagnetic potentials in the quantum theory', Phys. Rev. 115, 485 (1959)], that was tested by Tonomura et al., is a good approximation to the exact solution to the Schroedinger equation. This also proves that the electron, that is, represented by the exact solution, is not accelerated, in agreement with the recent experiment of Caprez et al. in 2007 ['Macroscopic test of the Aharonov-Bohm effect', Phys. Rev. Lett. 99, 210401 (2007)], that shows that the results of the Tonomura et al. experiments can not be explained by the action of a force. Under the assumption that the incoming free electron is a Gaussian wave packet, we estimate the exact solution to the Schroedinger equation for all times. We provide a rigorous, quantitative error bound for the difference in norm between the exact solution and the Aharonov-Bohm Ansatz. Our bound is uniform in time. We also prove that on the Gaussian asymptotic state the scattering operator is given by a constant phase shift, up to a quantitative error bound that we provide. Our results show that for intermediate size electron wave packets, smaller than the ones used in the Tonomura et al. experiments, quantum mechanics predicts the results observed by Tonomura et al. with an error bound smaller than 10
Scattering theory and the Aharonov-Bohm effect in quasiclassical physics
Research highlights: → Scattering Aharonov-Bohm effect. → Short-wavelength limit of scattered nonrelativistic particles. → Fraunhofer diffraction in the forward direction. → Fresnel diffraction in the forward region in conical space. → Enclosed magnetic flux is a gate for the propagation of quasiclassical particles. - Abstract: Scattering of a nonrelativistic quantum-mechanical particle by an impenetrable magnetic vortex is considered. The nonvanishing transverse size of the vortex is taken into account, and the limit of short, as compared to this size, wavelengths of the scattered particle is analyzed. We show that the scattering Aharonov-Bohm effect persists in the quasiclassical limit owing to the diffraction persisting in the short-wavelength limit. As a result, the vortex flux serves as a gate for the propagation of short-wavelength, almost classical, particles. This quasiclassical effect is more feasible to experimental detection in the case when space outside the vortex is conical.
Aharonov-Bohm effect for a fermion field in the acoustic black hole background
Anacleto, M A; Mohammadi, A; Passos, E
2016-01-01
In this paper we consider the dynamics of a massive spinor field in the background of the acoustic black hole spacetime and then compute the differential cross section through the use of the partial wave approach. We show that an effect similar to the gravitational Aharonov-Bohm effect occurs for massive fermion fields moving in this effective metric. We discuss the limiting cases and compare the results with the bosonic case.
Optical analogue of the Aharonov-Bohm effect using anisotropic media
We show that in the context of paraxial optics, which can be analyzed through a wave equation similar to the non-relativistic Schroedinger equation of quantum mechanics but replacing time t by spatial coordinate z, the existence of a vector potential A-perpendicular mimicking the magnetic vector potential in quantum mechanics is allowed by specific gauge symmetries of the optical field in a medium with anisotropic refractive index. In this way, we use Feynman's path integral to demonstrate an optical analogue of the quantum-mechanical Aharonov-Bohm effect, encouraging the search for another optical systems with analogies with more complex quantum field theories. -- Highlights: → The optical analogue of the Aharonov-Bohm effect is demonstrated using anisotropic media. → It follows from the gauge principle applied to the optical field in the paraxial regime. → Feynman's path integral formalism is used to obtain the main result, leading directly from geometric to physical optics.
Two impurity Kondo problem under Aharonov--Bohm and Aharonov--Casher Effects
Aono, Tomosuke
2006-01-01
We investigate electron transport under the two impurity Kondo problem with the Aharonov--Bohm and Aharonov--Casher effects. These interference effects induce the Ising-coupled Ruderman--Kittel--Kasuya--Yosida (RKKY) interaction. We discuss the inter- and intra-site spin conductance as well as charge conductance in the Kondo and the mixed-valence regimes using the slave boson mean field approximation.
Remark on the Connectedness of Space in the Experimental Devices of Aharonov-Bohm Effect
QIAN Shang-Wu; GU Zhi-Yu
2003-01-01
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.
The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams
Rizzi, Guido; Ruggiero, Matteo Luca
2003-01-01
The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation...
Reply to "Comment on `Role of potentials in the Aharonov-Bohm effect' "
Vaidman, Lev
2015-08-01
The preceding Comment challenged my claim that potentials might be just auxiliary mathematical tools and that they are not necessary for explaining physical phenomena. The Comment did not confront my explanation without the potentials of the Aharonov-Bohm effects that appeared in the original article, but stated that I cannot apply this explanation for seven other examples. In my reply, using my method, I provide explanations of one of the examples, show that two other examples are not relevant, and agree that the remaining examples require further analysis. However, I argue that none of the examples provides robust counterexamples to my claim, similar to the original Aharonov-Bohm setups which were explained in my article, so the Comment does not refute my claim.
The time-dependent non-Abelian Aharonov-Bohm effect
Bright, Max
2015-01-01
In this article, we study the {\\it time-dependent} Aharonov-Bohm effect for non-Abelian gauge fields. We use two well known time-dependent solutions to the Yang-Mills field equations to investigate the Aharonov-Bohm phase shift. For both of the solutions, we find a cancellation between the phase shift coming from the non-Abelian "magnetic" field and the phase shift coming from the non-Abelian "electric" field, which inevitably arises in time-dependent cases. We compare and contrast this cancellation for the time-dependent non-Abelian case to a similar cancellation which occurs in the time-dependent Abelian case. We postulate that this cancellation occurs generally in time-dependent situations for both Abelian and non-Abelian fields.
Spin accumulation assisted by the Aharonov-Bohm-Fano effect of quantum dot structures.
Gong, Wei-Jiang; Han, Yu; Wei, Guo-Zhu; Du, An
2012-01-01
: We investigate the spin accumulations of Aharonov-Bohm interferometers with embedded quantum dots by considering spin bias in the leads. It is found that regardless of the interferometer configurations, the spin accumulations are closely determined by their quantum interference features. This is mainly manifested in the dependence of spin accumulations on the threaded magnetic flux and the nonresonant transmission process. Namely, the Aharonov-Bohm-Fano effect is a necessary condition to achieve the spin accumulation in the quantum dot of the resonant channel. Further analysis showed that in the double-dot interferometer, the spin accumulation can be detailedly manipulated. The spin accumulation properties of such structures offer a new scheme of spin manipulation. When the intradot Coulomb interactions are taken into account, we find that the electron interactions are advantageous to the spin accumulation in the resonant channel. PMID:22985404
How the Test of Aharonov-Bohm Effect Was Initiated at Hitachi Laboratory
Osakabe, Nobuyuki
2014-01-01
I joined the Tonomura's team in 1980. Since then, I have seen his enthusiasm and creativity in science as a member of his team and later as director of the laboratory. I will discuss in this article how the industrially driven technologies met science at Hitachi Central Research Laboratory in the case of verification of the Aharonov-Bohm effect and other scientific achievements by Akira Tonomura.
Entanglement entropy as a witness of the Aharonov-Bohm effect in QFT
Arias, Raúl E; Casini, Horacio
2014-01-01
We study the dependence of the entanglement entropy with a magnetic flux, and show that the former quantity witnesses an Aharonov Bohm-like effect. In particular, we consider free charged scalar and Dirac fields living on a two dimensional cylinder and study how the entanglement entropy for a strip-like region on the surface of the cylinder is affected by a magnetic field enclosed by it.
Reply to "Comment on "Aharonov-Casher and Scalar Aharonov-Bohm Topological Effects""
Ma, Kai; Dulat, Sayipjamal
2013-01-01
In this Reply we argue that (i) the Hamiltonian, Eq. (17) in our paper (Phys. Rev. Lett. 108, 070405 (2012)), is definitely Lorentz invariant; (ii) the conditions of generating topological Aharonov-Casher(AC) and Scalar Aharonov-Bohm (SAB) effects are essential and physically meaningful; (iii) the Hamiltonians both in Phys. Rev. Lett. 74, 2847 (1995) and arXiv:1311.4011 are not suitable to describe the polarized spinor particles.
Coupling of Aharonov-Bohm and Aharonov-Casher effects at different particle spins
Coupling of Aharonov-Bohm and Aharonov-Casher topological effects is studied depending on the spin of moving particle and its orientation. Duality of wave functions occurs only at the absence of spin precession, that is, at a certain, maximal by the absolute value of its projection on the normal to the motion plane. Generalization for particles both with charge and anomalous magnetic moment is studied. 12 refs
Semenov, Andrew G.; Zaikin, Andrei D.
2010-01-01
We investigate the effect of electron-electron interactions on Aharonov-Bohm (AB) current oscillations in nanorings formed by a chain of metallic quantum dots. We demonstrate that electron-electron interactions cause electron dephasing thereby suppressing the amplitude of AB oscillations at all temperatures down to T=0. The crossover between thermal and quantum dephasing is found to be controlled by the ring perimeter. Our predictions can be directly tested in future experiments.
Tadić, M.; Čukarić, N.; Arsoski, V.; Peeters, F. M.
2010-01-01
The exciton states in strained (In,Ga)As nanorings embedded in a GaAs matrix are computed. The strain distribution is extracted from the continuum mechanical model, and the exact diagonalization approach is employed to compute the exciton states. Weak oscillations of the ground exciton state energy with the magnetic field normal to the ring are an expression of the excitonic Aharonov-Bohm effect. Those oscillations arise from anticrossings between the ground and the second exciton state and c...
Semenov, Andrew G.; Zaikin, Andrei D.
2009-01-01
We investigate the effect of electron-electron interactions on Aharonov-Bohm (AB) current oscillations in nanorings formed by a chain of metallic quantum dots. We demonstrate that electron-electron interactions cause electron dephasing thereby suppressing the amplitude of AB oscillations at all temperatures down to T=0. The crossover between thermal and quantum dephasing is found to be controlled by the ring perimeter. Our predictions can be directly tested in future experiments.
Observation of Scalar Aharonov-Bohm Effect with Longitudinally Polarized Neutrons
Lee, W. -T.; Motrunich, O.; Allman, B. E.; Werner, S. A.
1998-01-01
We have carried out a neutron interferometry experiment using longitudinally polarized neutrons to observe the scalar Aharonov-Bohm effect. The neutrons inside the interferometer are polarized parallel to an applied pulsed magnetic field B(t). The pulsed B field is spatially uniform so it exerts no force on the neutrons. Its direction also precludes the presence of any classical torque to change the neutron polarization.
Time-dependent Pauli equation in the presence of the Aharonov-Bohm effect
We use the Lewis-Riesenfeld theory to determine the exact form of the wavefunctions of a two-dimensional Pauli equation of a charged spin 1/2 particle with time-dependent mass and frequency in the presence of the Aharonov-Bohm effect and a two-dimensional time-dependent harmonic oscillator. We find that the irregular solution at the origin as well as the regular one contributes to the phase of the wavefunction
Time-dependent Pauli equation in the presence of the Aharonov-Bohm effect
Bouguerra, Y.; Bounames, A.; Maamache, M.; Saadi, Y.
2008-04-01
We use the Lewis-Riesenfeld theory to determine the exact form of the wavefunctions of a two-dimensional Pauli equation of a charged spin 1/2 particle with time-dependent mass and frequency in the presence of the Aharonov-Bohm effect and a two-dimensional time-dependent harmonic oscillator. We find that the irregular solution at the origin as well as the regular one contributes to the phase of the wavefunction.
Effects of nongauge potentials on the spin-1/2 Aharonov-Bohm problem
Some recent work has attempted to show that the singular solutions which are known to occur in the Dirac description of spin-1/2 Aharonov-Bohm scattering can be eliminated by the inclusion of strongly repulsive potentials inside the flux tube. It is shown here that these calculations are generally unreliable since they necessarily require potentials which lead to the occurrence of Klein's paradox. To avoid that difficulty the problem is solved within the framework of the Galilean spin-1/2 wave equation which is free of that particular complication. It is then found that the singular solutions can be eliminated provided that the nongauge potential is made energy dependent. The effect of the inclusion of a Coulomb potential is also considered with the result being that the range of flux parameter for which singular solutions are allowed is only one-half as great as in the pure Aharonov-Bohm limit. Expressions are also obtained for the binding energies which can occur in the combined Aharonov-Bohm-Coulomb system
Generalized Aharonov-Bohm experiments with neutrons
The Aharonov-Bohm effects are generally regarded as direct manifestations of the property, that potentials are affecting quantum systems in a way significantly different from the classical case. This paper searches for generalizations for the neutron case, where still some of the features of the original Aharonov-Bohm effects are maintained. This is based on operational analogy and does not involve any interpretive or epistemological questions. The author identifies operationally significant features of the Aharonov-Bohm effects with a thorough operational analysis. The electric and the magnetic Aharonov-Bohm effects are analyzed separately; this procedure leads to the identification of common features
We study the persistent currents induced by both the Aharonov-Bohm and Aharonov-Casher effects in a one-dimensional mesoscopic ring coupled to a sidebranch quantum dot at Kondo resonance. For privileged values of the Aharonov-Bohm-Casher fluxes, the problem can be mapped onto an integrable model, exactly solvable by a Bethe ansatz. In the case of a pure magnetic Aharonov-Bohm flux, we find that the presence of the quantum dot has no effect on the persistent current. In contrast, the Kondo resonance interferes with the spin-dependent Aharonov-Casher effect to induce a current which, in the strong-coupling limit, is independent of the number of electrons in the ring
Grochol, M.; Grosse, F.; Zimmermann, R.
2006-09-01
The optical exciton Aharonov-Bohm effect—i.e., an oscillatory component in the energy of optically active (bright) states—is investigated in nanorings. It is shown that a small effective electron mass, strong confinement of the electron, and high barrier for the hole, achieved, e.g., by an InAs nanoring embedded in an AlGaSb quantum well, are favorable for observing the optical exciton Aharonov-Bohm effect. The second derivative of the exciton energy with respect to the magnetic field is utilized to extract Aharonov-Bohm oscillations even for the lowest bright state unambiguously. A connection between the theories for infinitesimal narrow and finite width rings is established. Furthermore, the magnetization is compared to the persistent current, which oscillates periodically with the magnetic field and confirms thus the nontrivial (connected) topology of the wave function in the nanoring.
Exact equivalence of spin-1/2 Aharonov-Bohm and Aharonov-Casher effects
It is shown that there is an exact equivalence between the Aharonov-Bohm effect for spin-1/2 particles and the Aharonov-Casher effect. The demonstration of this precise relationship between the two is seen furthermore to be independent of whether relativistic or nonrelativistic kinematics are used. The only remaining substantive distinction between the two effects may well be the fact that the scattering cross section for polarized beams has a considerably greater sturcture in the Aharonov-Casher case despite the mathematical equivalence of the scattering amplitudes for the two effects
Aharonov-Bohm and Aharonov-Casher Effects: Connections to Dynamics of Topological Singularities
Ao, P.; Niu, Q.
1998-01-01
We analyze the physical processes involved in the Aharonov-Bohm (A-B) and the Aharonov-Casher (A-C) effects, showing that an incomplete A-B effect knowledge can lead a totally wrong conclusion on the A-C effect. Based on this we demonstrate that the Magnus force, the net force, is the only transverse force on a moving vortex, in analogous to the net charge in A-C effect. This conclusion has been arrived both theoretically and experimentally.
Grochol, M.; Grosse, F.; Zimmermann, R.
2005-01-01
The optical exciton Aharonov-Bohm effect, i. e. an oscillatory component in the energy of optically active (bright) states, is investigated in nanorings. It is shown that a small effective electron mass, strong confinement of the electron, and high barrier for the hole, achieved e. g. by an InAs nanoring embedded in an AlGaSb quantum well, are favorable for observing the optical exciton Aharonov-Bohm effect. The second derivative of the exciton energy with respect to the magnetic field is uti...
Interrelations Between the Neutron's Magnetic Interactions and the Magnetic Aharonov-Bohm Effect
Comay, E
1999-01-01
It is proved that the phase shift of a polarized neutron interacting with a spatially uniform time-dependent magnetic field, demonstrates the same physical principles as the magnetic Aharonov-Bohm effect. The crucial role of inert objects is explained, thereby proving the quantum mechanical nature of the effect. It is also proved that the nonsimply connectedness of the field-free region is not a profound property of the system and that it cannot be regarded as a sufficient condition for a nonzero phase shift.
Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields
Hosseini Mansoori, Seyed Ali; Mirza, Behrouz
2016-04-01
We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of SU (N) generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.
Kondo effect in transport through Aharonov-Bohm and Aharonov-Casher interferometers
Lobos, A. M.; Aligia, A. A.
2009-01-01
We derive the extension of the Hubbard model to include Rashba spin-orbit coupling that correctly describes Aharonov-Bohm and Aharonov-Casher phases in a ring under applied magnetic and electric fields. When the ring is connected to conducting leads, we develop a formalism that is able to describe both, Kondo and interference effects. We find that in the Kondo regime, the spin-orbit coupling reduces strongly the conductance from the unitary limit. This effect in combination with the magnetic ...
Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields
Mansoori, Seyed Ali Hosseini
2016-01-01
We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of $SU(N)$ generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.
Kondo effect in transport through Aharonov-Bohm and Aharonov-Casher interferometers
We derive the extension of the Hubbard model to include Rashba spin-orbit coupling that correctly describes Aharonov-Bohm and Aharonov-Casher phases in a ring under applied magnetic and electric fields. When the ring is connected to conducting leads, we develop a formalism that is able to describe both, Kondo and interference effects. We find that in the Kondo regime, the spin-orbit coupling reduces strongly the conductance from the unitary limit. This effect in combination with the magnetic flux, can be used to produce spin polarized carriers.
Aharonov-Bohm effect for an exciton in a finite width nano-ring
Palmero, F.; Dorignac, J.; Eilbeck, J. C.; Romer, R. A.
2005-01-01
We study the Aharonov-Bohm effect for an exciton on a nano-ring using a 2D attractive fermionic Hubbard model. We extend previous results obtained for a 1D ring in which only azimuthal motion is considered, to a more general case of 2D annular lattices. In general, we show that the existence of the localization effect, increased by the nonlinearity, makes the phenomenon in the 2D system similar to the 1D case. However, the introduction of radial motion introduces extra frequencies, different ...
Absence of the Electric Aharonov-Bohm Effect due to Induced Charges
Rui-Feng Wang
2015-01-01
This paper states that the induced charge should not be neglected in the electric Aharonov-Bohm (A-B) effect. If the induced charge is taken into account, the interference pattern of the moving charge will not change with the potential difference between the two metal tubes. It means that the scalar potential itself can not affect the phase of the moving charge, and the true factor affecting the phase of the moving charge is the energy of the system including the moving charge and the induced...
Absence of the Electric Aharonov-Bohm Effect due to Induced Charges
Wang, Rui-Feng
2015-09-01
This paper states that the induced charge should not be neglected in the electric Aharonov-Bohm (A-B) effect. If the induced charge is taken into account, the interference pattern of the moving charge will not change with the potential difference between the two metal tubes. It means that the scalar potential itself can not affect the phase of the moving charge, and the true factor affecting the phase of the moving charge is the energy of the system including the moving charge and the induced charge.
Non-radiating sources, dynamic anapole and Aharonov-Bohm effect
Nemkov, Nikita A; Fedotov, Vassily A
2016-01-01
We show that any non-radiating source can be represented by a combination of identical, spatially localized distributions of electric and toroidal point dipoles. One of the implications is that at every point of an arbitrary non-radiating source there exists a simple universal relation between the electric and toroidal dipole moments. We also present simple means of describing non-radiating sources and discuss a possible scenario for observing the time-dependent version of the Aharonov-Bohm effect in such systems.
We consider the motion of free relativistic particles in multiply connected spaces. We show that if one of the spatial dimensions has the topology of a circle then the D dimensional spacetime is compactified to D-1 dimensions and the particle mass increases by an amount which is proportional to a quantum phase factor and inversely proportional to the radius of the circle. We also consider the relativistic Aharonov-Bohm effect and we show that the interference pattern is a universal characteristic due only to the topological properties of the experimental situation and not to the intrinsic properties of the particle. The propagators are calculated in both situations. (author)
Geometric phases in quantum mechanics and the dual Aharonov-Bohm effect
Full text: In the year of 1959, Y. Aharonov and D. Bohm published a paper discussing the importance of the electromagnetic potentials in quantum mechanics, not only as a mathematical tool but as an object with physical significance. In this paper they propose an experiment in which a measurable phase change can be observed in the wavefunction of the electron passing by a long thin solenoid due to the presence of the magnetic potential, even in the absence of magnetic fields. Since then, the effect became known as the Aharonov-Bohm (AB) effect. Although it was not widely discussed at the time of the above publication, the AB effect can be understood as a specific case of a broader class of phenomena generally known as geometric phases. A paper was published in 1984 by the british physicist Michael Berry bringing about a widespread discussion on the importance of geometric phases and their appearance and applications in a great number of physical systems and in technologies such as topological quantum computation, for instance. In this work we discuss the appearance of geometric phases in both adiabatic, as discussed by Berry, and general evolution of quantum systems. Some modern applications are presented and the approach of geometrical phases is used to study some proposed implementations of the dual Aharonov-Bohm effect, built upon duality transformations on Maxwell's Equations. (author)
Aharonov-Bohm and Aharonov-Casher tunneling effects and edge states in double-barrier structures
The simultaneous occurrence of Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects due to edge states in double-barrier two-dimensional wires formed by an electrostatic confinement potential, in the quantum Hall effect regime, is discussed. The AC effect is manifested via a shift of the AB conductance oscillations, and a method for measurement of the effect is proposed
Excitonic Aharonov-Bohm effect: Unstrained versus strained type-I semiconductor nanorings
Tadić, M.; Čukarić, N.; Arsoski, V.; Peeters, F. M.
2011-09-01
We study how mechanical strain affects the magnetic field dependence of the exciton states in type-I semiconductor nanorings. Strain spatially separates the electron and hole in (In,Ga)As/GaAs nanorings which is beneficial for the occurrence of the excitonic Aharonov-Bohm (AB) effect. In narrow strained (In,Ga)As/GaAs nanorings the AB oscillations in the exciton ground-state energy are due to anticrossings with the first excited state. No such AB oscillations are found in unstrained GaAs/(Al,Ga)As nanorings irrespective of the ring width. Our results are obtained within an exact numerical diagonalization scheme and are shown to be accurately described by a two-level model with off-diagonal coupling t. The later transfer integral expresses the Coulomb coupling between states of electron-hole pairs. We also found that the oscillator strength for exciton recombination in (In,Ga)As/GaAs nanorings exhibits AB oscillations, which are superimposed on a linear increase with magnetic field. Our results agree qualitatively with recent experiments on the excitonic Aharonov-Bohm effect in type-I (In,Ga)As/GaAs nanorings.
Gaussian Curvature and Global effects : gravitational Aharonov-Bohm effect revisited
Nouri-Zonoz, M
2013-01-01
Using the Gauss-Bonnet formula, integral of the Gaussian curvature over a 2-surface enclosed by a curve in the asymptotically flat region of a static spacetime was found to be a measure of a gravitational analogue of Aharonov-Bohm effect by Ford and Vilenkin in the linearized regime. Employing the 1+3 formulation of spacetime decomposition we study the same effect in the context of full Einstein field equations for stationary spacetimes. Applying our approach to static tube-like and cylindrical distributions of dust not only we recover their result but also obtain an extra term which is interpreted to be representing the classical version of the Colella-Overhauser-Werner effect (the COW experiment).
Probing the noncommutative effects of phase space in the time-dependent Aharonov-Bohm effect
Ma, Kai; Yang, Huan-Xiong
2016-01-01
We study the noncommutative corrections on the time-dependent Aharonov-Bohm effect when both the coordinate-coordinate and momentum-momentum noncommutativities are considered. This study is motivated by the recent observation that there is no net phase shift in the time-dependent AB effect on the ordinary space, and therefore tiny derivation from zero can indicate new physics. The vanishing of the time-dependent AB phase shift on the ordinary space is preserved by the gauge and Lorentz symmetries. However, on the noncomutative phase space, while the ordinary gauge symmetry can be kept by the Seiberg-Witten map, but the Lorentz symmetry is broken. Therefore nontrivial noncommutative corrections are expected. We find there are three kinds of noncommutative corrections in general: 1) $\\xi$-dependent correction which comes from the noncommutativity among momentum operators; 2) momentum-dependent correction which is rooted in the nonlocal interactions in the noncommutative extended model; 3) momentum-independent c...
Trammel, G. T.
1964-01-01
Aharonov-bohm paradox involving charge particle interaction with stationary current distribution showing that vector potential term in canonical momenta expression represents electromagnetic field momentum
Thermoelectric effect in an Aharonov-Bohm ring with an embedded quantum dot.
Zheng, Jun; Chi, Feng; Lu, Xiao-Dong; Zhang, Kai-Cheng
2012-01-01
Thermoelectric effect is studied in an Aharonov-Bohm interferometer with an embedded quantum dot (QD) in the Coulomb blockade regime. The electrical conductance, electron thermal conductance, thermopower, and thermoelectric figure-of-merit are calculated by using the Keldysh Green's function method. It is found that the figure-of-merit ZT of the QD ring may be quite high due to the Fano effect originated from the quantum interference effect. Moreover, the thermoelectric efficiency is sensitive to the magnitude of the dot-lead and inter-lead coupling strengthes. The effect of intradot Coulomb repulsion on ZT is significant in the weak-coupling regime, and then large ZT values can be obtained at rather high temperature. PMID:22369454
Against a proposed alternative explanation of the Aharonov-Bohm effect
The Aharonov-Bohm (AB) effect is understood to demonstrate that the Maxwell fields can act nonlocally in some situations. However it has been suggested from time to time that the AB effect is somehow a consequence of a local classical electromagnetic field phenomenon involving energy that is temporarily stored in the overlap between the external field and the field of which the beam particle is the source. That idea was shown in the past not to work for some models of the source of the external field. Here a more general proof is presented for the magnetic AB effect to show that the overlap energy is always compensated by another contribution to the energy of the magnetic field in such a way that the sum of the two is independent of the external flux. Therefore no such mechanism can underlie the AB effect.
Combined Aharonov-Bohm and Zeeman spin-polarization effects in a double quantum dot ring
A mesoscale Aharonov-Bohm (AB) ring with a quantum dot (QD) embedded in each arm is computationally modeled for unique transmission properties arising from a combination of AB effects and Zeeman splitting of the QD energy levels. A tight-binding Hamiltonian is solved, providing analytical expressions for the transmission as a function of system parameters. Transmission resonances with spin-polarized output are presented for cases involving either a perpendicular field, or a parallel field, or both. The combination of the AB-effect with Zeeman splitting allows sensitive control of the output resonances of the device, manifesting in spin-polarized states which separate and cross as a function of applied field. In the case with perpendicular flux, the AB-oscillations exhibit atypical non-periodicity, and Fano-type resonances appear as a function of magnetic flux due to the flux-dependent shift in the QD energy levels via the Zeeman effect.
Aharonov-Bohm effect in the tunnelling of a quantum rotor in a linear Paul trap.
Noguchi, Atsushi; Shikano, Yutaka; Toyoda, Kenji; Urabe, Shinji
2014-01-01
Quantum tunnelling is a common fundamental quantum mechanical phenomenon that originates from the wave-like characteristics of quantum particles. Although the quantum tunnelling effect was first observed 85 years ago, some questions regarding the dynamics of quantum tunnelling remain unresolved. Here we realize a quantum tunnelling system using two-dimensional ionic structures in a linear Paul trap. We demonstrate that the charged particles in this quantum tunnelling system are coupled to the vector potential of a magnetic field throughout the entire process, even during quantum tunnelling, as indicated by the manifestation of the Aharonov-Bohm effect in this system. The tunnelling rate of the structures periodically depends on the strength of the magnetic field, whose period is the same as the magnetic flux quantum φ0 through the rotor [(0.99 ± 0.07) × φ0]. PMID:24820051
The Aharonov-Bohm effect and fractional statistics of distinguishable particles
In two-dimensional space, the topological coupling arising between charged particles with attached magnetic fluxes, via the Aharonov-Bohm effect, causes distinguishable particles to effectively acquire quantum statistics: a nontrivial quantum phase is generated when a particle of one species encircles one of a different species. We discuss a number of exact and numerical results concerning distinguishable particles with fractional statistics. Just like for anyons, the spectrum of such particles confined to the lowest Landau level of a strong magnetic field can be found exactly. Then a system of particles in the presence of static magnetic fluxes (equivalent to particles with infinite mass) is considered, and the low-lying states of one particle in the presence of two fluxes and two particles in the presence of one flux are analyzed.
The manifestly covariant Aharonov-Bohm effect in terms of the 4D fields
Ivezic, Tomislav
2014-01-01
In this paper it is presented a manifestly covariant formulation of the Aharonov-Bohm (AB) phase difference for the magnetic AB effect . This covariant AB phase is written in terms of the Faraday 2-form F and using the decomposition of F in terms of the electric and magnetic fields as four-dimensional (4D) geometric quantities. It is shown that there is a static electric field outside a stationary solenoid with resistive conductor carrying steady current, which causes that the AB phase difference in the magnetic AB effect may be determined by the electric part of the covariant expression, i.e. by the local influence of the 4D electric field and not, as generally accepted,in terms of nonzero vector potential.
Aharonov-Bohm effect in the tunnelling of a quantum rotor in a linear Paul trap
Noguchi, Atshushi; Toyoda, Kenji; Urabe, Shinji
2014-01-01
Quantum tunnelling is a common fundamental quantum-mechanical phenomenon that originates from the wave-like characteristics of quantum particles. Although the quantum-tunnelling effect was first observed 85 years ago, some questions regarding the dynamics of quantum tunnelling remain unresolved. Here, we realise a quantum-tunnelling system using two-dimensional ionic structures in a linear Paul trap. We demonstrate that the charged particles in this quantum-tunnelling system are coupled to the vector potential of a magnetic field throughout the entire process, even during quantum tunnelling, as indicated by the manifestation of the Aharonov-Bohm effect in this system. The tunnelling rate of the structures periodically depends on the strength of the magnetic field, whose period is the same as the magnetic-flux quantum $\\phi_0$ through the rotor [($0.99 \\pm 0.07)\\times \\phi_0$].
Multiple-path Quantum Interference Effects in a Double-Aharonov-Bohm Interferometer
Yang XF
2010-01-01
Full Text Available Abstract We investigate quantum interference effects in a double-Aharonov-Bohm (AB interferometer consisting of five quantum dots sandwiched between two metallic electrodes in the case of symmetric dot-electrode couplings by the use of the Green’s function equation of motion method. The analytical expression for the linear conductance at zero temperature is derived to interpret numerical results. A three-peak structure in the linear conductance spectrum may evolve into a double-peak structure, and two Fano dips (zero conductance points may appear in the quantum system when the energy levels of quantum dots in arms are not aligned with one another. The AB oscillation for the magnetic flux threading the double-AB interferometer is also investigated in this paper. Our results show the period of AB oscillation can be converted from 2π to π by controlling the difference of the magnetic fluxes threading the two quantum rings.
Aharonov-Bohm effect of excitons in nano-rings
Hu, Hui; Zhu, Jia-Lin; Li, Dai-Jun; Xiong, Jia-Jiong
2000-01-01
The magnetic field effects on excitons in an InAs nano-ring are studied theoretically. By numerically diagonalizing the effective-mass Hamiltonian of the problem, which can be separated into terms in centre-of-mass and relative coordinates, we calculate the low-lying exciton energy levels and oscillator strengths as a function of the width of the ring and the strength of the external magnetic field. The analytical results are obtained for a narrow-width nano-ring in which the radial motion is...
Aharonov-Bohm effect in curved space and cosmic strings
The paper deals with the development of the theory of nonrelativistic particle scattering in the cosmic string field, which is considered as a registration of magnetic and gravitation strings. The effects, which are caused by the finite nature of the transverse parameters of the strings, are taken into account making sufficiently general assumptions about the distribution of the magnetic field and space curvature inside the string. It is shown that in a certain region of angles the differential scattering section significantly depends on the string magnetic flux value at all absolute values of the bombarding particle wind vector. 34 refs
Aharonov-Bohm effect in an electron-hole graphene ring system
D. Smirnov; Schmidt, H; Haug, R. J.
2012-01-01
Aharonov-Bohm oscillations are observed in a graphene quantum ring with a top gate covering one arm of the ring. As graphene is a gapless semiconductor this geometry allows to study not only the quantum interference of electrons with electrons or holes with holes but also the unique situation of quantum interference between electrons and holes. The period and amplitude of the observed Aharonov-Bohm oscillations are independent of the sign of the applied gate voltage showing the equivalence be...
Maslov, A. V.; Citrin, D. S.
2003-03-01
This work demonstrates that the Aharonov-Bohm effect for excitons, practically indistinguishable from the numerical noise without an applied electric field, becomes clearly evident in the optical absorption once the electric field is applied in the plane containing the nanoring. The enhancement arises as a result of the field-induced delocalization of the relative electron-hole motion around the entire ring. The excitonic effects are essential to describe even qualitatively the absorption spectra.
2D Pauli Equation with Hulthén Potential in the Presence of Aharonov-Bohm Effect
N.Ferkous; A.Bounames
2013-01-01
The 2D Pauli equation with Hulthén potential for spin-1/2 particle in the presence of Aharonov-Bohm (AB) field is solved analytically,on the assumption that an effective approximation is used for the centrifugai term.Singular and regular solutions of the problem are obtained.It is shown that the AB field lifts the degeneracy of the energy levels.The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case.When the screening parameter vanishes,it is shown that the obtained energy spectrum becomes the same as that of the Aharonov-Bohm Coulomb problem.
CHEN Bao-Ju; CHEN Xiong-Wen; SHI Zhen-Gang; ZHU Xi-Xiang; SONG Ke-Hui; WU Shao-Quan
2007-01-01
We theoretically investigate the properties of the ground state of the strongly correlated T-shaped double quantum dots embedded in an Aharonov-Bohm ring in the Kondo regime by means of the one-impurity Anderson Hamiltonian.It is found that in this system,the persistent current depends sensitively on the parity and size of the ring.With the increase of interdot coupling,the persistent current is suppressed due to the enhancing Fano interference weakening the Kondo effect.Moreover,when the spin of quantum dot embedded in the aharonovBohm ring is screened,the persistent current peak is not affected by interdot coupling.Thus this model may be a new candidate for detecting Kondo screening cloud.
Valley Zeeman energy in monolayer MoS2 quantum rings: Aharonov-Bohm effect
Oliveira, D.; Fu, Jiyong; Villegas-Lelovsky, L.; Dias, A. C.; Qu, Fanyao
2016-05-01
We investigate the valley Zeeman energy (VZE) in monolayer MoS2 quantum rings, subjected to a magnetic flux Φ only passing through a hole region enclosed by the inner circle of the ring. To gain insight on our numerical outcomes for finite two-dimensional rings, an analytic solution in the one-dimensional limit (zero ring width) is also presented. Although no magnetic field is applied inside the ring region, we observe finite VZEs. Interestingly, in contrast to the usual linear scenario, the VZE of the rings exhibits an oscillatory dependence on Φ with possible vanishing valley Zeeman effect even in a nonzero magnetic flux due to Aharonov-Bohm type effect. On the other hand, within one period of oscillations the VZE increases linearly with Φ . Furthermore, for a given magnetic flux, the valley Zeeman effect is more pronounced in a ring with a stronger quantum confinement. Thus the VZE can be tuned by either magnetic flux or ring confinement or both of them. This opens a new route for controlling the valley Zeeman effect using a nonmagnetic means.
Wang, Dehua
2014-09-01
The Aharonov-Bohm (AB) effect in the photodetachment microscopy of the H- ions in an electric field has been studied on the basis of the semiclassical theory. After the H- ion is irradiated by a laser light, they provide a coherent electron source. When the detached electron is accelerated by a uniform electric field, two trajectories of a detached electron which run from the source to the same point on the detector, will interfere with each other and lead to an interference pattern in the photodetachment microscopy. After the solenoid is electrified beside the H- ion, even though no Lorentz force acts on the electron outside the solenoid, the photodetachment microscopy interference pattern on the detector is changed with the variation in the magnetic flux enclosed by the solenoid. This is caused by the AB effect. Under certain conditions, the interference pattern reaches the macroscopic dimensions and could be observed in a direct AB effect experiment. Our study can provide some predictions for the future experimental study of the AB effect in the photodetachment microscopy of negative ions.
The Aharonov-Bohm effect in a spatially confining theory based on a turbulent fluid
Antonov, Dmitri
2012-01-01
Wilson loops in a turbulent fluid are shown to respect a specific area law corresponding to the Kolmogorov scaling. This law leads to the condensation of a complex-valued scalar field minimally coupled to the velocity field. We use this finding to estimate a v.e.v. of the dual Higgs field, which appears in the hydrodynamic description of a spatially confining dual Landau-Ginzburg theory. The temperature dependence of all other parameters of this theory is found upon a comparison with the spatial string tension and the chromo-magnetic vacuum correlation length of the Yang-Mills gluon plasma. In particular, a nonperturbative contribution to the shear viscosity of the dual fluid comes out exponentially suppressed with temperature. Interactions of the dual Abrikosov vortices with excitations of the fluid yield a long-range Aharonov-Bohm effect. This effect is shown to take place for all but calculated discrete values of the product of the kinematic viscosity of the fluid to the coupling constant of the dual Higgs...
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A W; Kwek, Leong Chuan
2014-01-01
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions. PMID:25103877
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan
2014-08-01
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a ``hairline'' solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.
Effect of vacuum polarization of charged massive fermions in an Aharonov-Bohm field
Khalilov, V.R. [M.V. Lomonosov Moscow State University, Faculty of Physics, Moscow (Russian Federation)
2014-09-15
The effect of vacuum polarization of charged massive fermions in an Aharonov-Bohm (AB) potential in 2 + 1 dimensions is investigated. The causal Green function of the Dirac equation with the AB potential is represented via the regular and irregular solutions of the two-dimensional radial Dirac equation. It is shown that the vacuum current density contains the contribution from free filled states of the negative energy continuum as well as that from a bound unfilled state, which can emerge in the above background due to the interaction of the fermion's spin magnetic moment with the AB magnetic field, while the induced charge density contains only the contribution from the bound state. The expressions for the vacuum charge and induced current densities are obtained (recovered for massless fermions) for the graphene in the field of infinitesimally thin solenoid perpendicular to the plane of a sample. We also find the bound state energy as a function of magnetic flux, fermion spin, and the radius of solenoid, and we discuss the role of the so-called self-adjoint extension parameter and determine it in terms of the physics of the problem. (orig.)
NonAbelian Vortices, Large Winding Limits and Aharonov-Bohm Effects
Bolognesi, Stefano; Konishi, Kenichi
2015-01-01
Remarkable simplification arises from considering vortex equations in the large winding limit. This was recently used in [1] to display all sorts of vortex zeromodes, the orientational, translational, fermionic as well as semi-local, and to relate them to the apparently distinct phenomena of the Nielsen-Olesen-Ambjorn magnetic instabilities. Here we extend these analyses to more general types of BPS nonAbelian vortices, taking as a prototype a system with gauged U(1) x SU(N) x SU(N) symmetry where the VEV of charged scalar fields in the bifundamental representation breaks the symmetry to SU(N)_{l+r} . The presence of the massless SU(N)_{l+r} gauge fields in 4D bulk introduces all sorts of non-local, topological phenomena such as the nonAbelian Aharonov-Bohm effects, which in the theory with global SU(N)_r group (g_r=0) are washed away by the strongly fluctuating orientational zeromodes in the worldsheet. Physics changes qualitatively at the moment the right gauge coupling constant g_r is turned on.
Spin Filter Based on an Aharonov-Bohm Interferometer with Rashba Spin-Orbit Effect
FANG Ming; SUN Lian-Liang
2008-01-01
We propose a spin filter based on both the quantum interference and the Rashba spin-orbit (RSO) effects. This spin filter consists of a Aharonov-Bohm (AB) interferometer with two quantum dots (QDs) inserted in its arms.The influences of a magnetic flux ψ threading through the AB ring and the RSO interaction inside the two QDs are taken into account by using the nonequilibrium Green's function technique. Due to the existence of the RSO interaction, the electrons flowing through different arms of the ring will acquire a spin-dependent phase factor in the linewidth matrix elements. This phase factor, combined with the influence of the magnetic flux, will induce a spin-dependent electron transport through the device. Moreover, we show that by tuning the magnetic flux,the RSO strength and the inter-dot tunnelling coupling strength, a pure spin-up or spin-down conductance can be obtained when a spin-unpolarized current is injected from the external leads, which can be used to filter the electron spin.
Effect of vacuum polarization of charged massive fermions in an Aharonov-Bohm field
The effect of vacuum polarization of charged massive fermions in an Aharonov-Bohm (AB) potential in 2 + 1 dimensions is investigated. The causal Green function of the Dirac equation with the AB potential is represented via the regular and irregular solutions of the two-dimensional radial Dirac equation. It is shown that the vacuum current density contains the contribution from free filled states of the negative energy continuum as well as that from a bound unfilled state, which can emerge in the above background due to the interaction of the fermion's spin magnetic moment with the AB magnetic field, while the induced charge density contains only the contribution from the bound state. The expressions for the vacuum charge and induced current densities are obtained (recovered for massless fermions) for the graphene in the field of infinitesimally thin solenoid perpendicular to the plane of a sample. We also find the bound state energy as a function of magnetic flux, fermion spin, and the radius of solenoid, and we discuss the role of the so-called self-adjoint extension parameter and determine it in terms of the physics of the problem. (orig.)
Aharonov-Bohm effects on bright and dark excitons in carbon nanotubes
A short-range part of the Coulomb interaction causes splitting and shift of excitons due to exchange interaction and mixing between different valleys in semiconducting carbon nanotubes. In the absence of a magnetic flux only a single exciton is optically active (bright) and all others are inactive (dark). Two bright excitons appear in the presence of an Aharonov- Bohm magnetic flux
Tadić, M.; Arsoski, V.; Čukarić, N.; Peeters, F. M.
2013-12-01
The excitonic Aharonov-Bohm oscillations in type-I nanorings are found to be caused by anticrossings between exciton states. These anticrossings are analyzed by a tight-binding-like model of exciton states. The criteria for the existence of the excitonic Aharonov-Bohm oscillations are formulated. For nanorings of realistic width and height, the range of values of the inner radius where the excitonic Aharonov-Bohm oscillations exist is found.
Aharonov-Bohm oscillations in the local density of states
A. Cano; Paul, I
2009-01-01
The scattering of electrons with inhomogeneities produces modulations in the local density of states of a metal. We show that electron interference contributions to these modulations are affected by the magnetic field via the Aharonov-Bohm effect. This can be exploited in a simple STM setup that serves as an Aharonov-Bohm interferometer at the nanometer scale.
Polarized excitons in nanorings and the `optical' Aharonov-Bohm effect
Govorov, A. O.; Ulloa, S. E.; Karrai, K.; Warburton, R. J.
2002-01-01
The quantum nature of matter lies in the wave function phases that accumulate while particles move along their trajectories. A prominent example is the Aharonov-Bohm phase, which has been studied in connection with the conductance of nanostructures. However, optical response in solids is determined by neutral excitations, for which no sensitivity to magnetic flux would be expected. We propose a new mechanism for the topological phase of a neutral particle, a polarized exciton confined to a se...
Aharonov-Bohm phase for an electromagnetic wave background
Bright, Max; Singleton, Douglas; Yoshida, Atsushi
2015-09-01
The canonical Aharonov-Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a charged particle moving in time-dependent potentials. In particular, we focus on the case of a charged particle moving in the time-varying field of a plane electromagnetic wave. We work out the Aharonov-Bohm phase using both the potential (i.e. oint A_μ dx ^μ ) and the field (i.e. 1/2int F_{μ ν } dσ ^{μ ν }) forms of the Aharonov-Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space-time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov-Bohm effect could be observed.
Aharonov-Bohm phase for an electromagnetic wave background
The canonical Aharonov-Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a charged particle moving in time-dependent potentials. In particular, we focus on the case of a charged particle moving in the time-varying field of a plane electromagnetic wave. We work out the Aharonov-Bohm phase using both the potential (i.e. circular integral Aμ dxμ) and the field (i.e. (1)/(2) ∫ Fμνdσμν) forms of the Aharonov-Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space-time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov-Bohm effect could be observed. (orig.)
Aharonov-Bohm phase for an electromagnetic wave background
Bright, Max [California State University Fresno, Department of Physics, Fresno, CA (United States); Singleton, Douglas [California State University Fresno, Department of Physics, Fresno, CA (United States); UNESP-Univ. Estadual Paulista, ICTP South American Institute for Fundamental Research, Sao Paulo, SP (Brazil); Yoshida, Atsushi [University of Virginia, Department of Physics, Charlottesville, VA (United States); Hue University College of Education, Hue (Viet Nam)
2015-09-15
The canonical Aharonov-Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a charged particle moving in time-dependent potentials. In particular, we focus on the case of a charged particle moving in the time-varying field of a plane electromagnetic wave. We work out the Aharonov-Bohm phase using both the potential (i.e. circular integral A{sub μ} dx{sup μ}) and the field (i.e. (1)/(2) ∫ F{sub μν}dσ{sup μν}) forms of the Aharonov-Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space-time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov-Bohm effect could be observed. (orig.)
Aharonov-Bohm Constraint for Fusion
Yahalom, Asher
It was shown that an Aharonov-Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables. If a MHD flow has a non trivial topology some of the functions appearing in the MHD Lagrangian are non-single valued. Some of those functions are analogue to the phases in the AB celebrated effect. While the manifestation of the quantum AB effect is in interference fringe patterns, the manifestation of the MHD Aharonov-Bohm effect is through a new dynamical conservation law. This local conservation law will be shown to constrain the dynamics of MHD flows including fusion scenarios. Bibliography
Quantum Faraday Effect in Double-Dot Aharonov-Bohm Ring
Kang, Kicheon
2011-01-01
We investigate Faraday's law of induction manifested in the quantum state of Aharonov-Bohm loops. In particular, we propose a flux-switching experiment for a double-dot AB ring to verify the phase shift induced by Faraday's law. We show that the induced {\\em Faraday phase} is geometric and nontopological. Our study demonstrates that the relation between the local phases of a ring at different fluxes is not arbitrary but is instead determined by Faraday's inductive law, which is in strong cont...
Instanton Aharonov-Bohm effect and macroscopic quantum coherence in charge-density-wave systems
It is predicted that in a charge-density-wave (CDW) ring-shaped conductor, placed in an external vector-potential field, there should appear a new Aharonov-Bohm contribution to the magnetic susceptibility and the electrical conductivity oscillating as a function of the flux with the period φ0=hc/2e. This contribution arises from instanton transitions between degenerate vacua of the CDW-condensate and is the solid-state realization of θ-vacuum in the quantum field theory. The period transforms into φ0/N in N strongly correlated parallel CDW chains. (author). 27 refs, 2 figs
Schütz, G; Rembold, A; Pooch, A; Prochel, H; Stibor, A
2015-11-01
We propose an experiment for the first proof of the type I electric Aharonov-Bohm effect in an ion interferometer for hydrogen. The performances of three different beam separation schemes are simulated and compared. The coherent ion beam is generated by a single atom tip (SAT) source and separated by either two biprisms with a quadrupole lens, two biprisms with an einzel-lens or three biprisms. The beam path separation is necessary to introduce two metal tubes that can be pulsed with different electric potentials. The high time resolution of a delay line detector allows to work with a continuous ion beam and circumvents the pulsed beam operation as originally suggested by Aharonov and Bohm. We demonstrate that the higher mass and therefore lower velocity of ions compared to electrons combined with the high expected SAT ion emission puts the direct proof of this quantum effect for the first time into reach of current technical possibilities. Thereby a high detection rate of coherent ions is crucial to avoid long integration times that allow the influence of dephasing noise from the environment. We can determine the period of the expected matter wave interference pattern and the signal on the detector by determining the superposition angle of the coherent partial beams. Our simulations were tested with an electron interferometer setup and agree with the experimental results. We determine the separation scheme with three biprisms to be most efficient and predict a total signal acquisition time of only 80s to measure a phase shift from 0 to 2π due to the electric Aharonov-Bohm effect. PMID:26188995
Fano effect in the Andreev reflection of the Aharonov-Bohm-Fano ring with Majorana bound states
Jiang, Cui; Zheng, Yi-Song
2015-06-01
The Andreev reflection in an Aharonov-Bohm-Fano ring induced by Majorana bound states (MBSs) is theoretically investigated. We find that compared with the Fano effect in the normal electron tunneling process, the Fano effect here is more determined by the structural parameters, i.e., the quantum dot level, the dot-MBS coupling, and the dot-MBS and MBS-lead couplings. By transforming the ring into its Nambu representation, we present a comprehensive analysis about the quantum interference in the Andreev reflection, and then explain the reason for the occurrence of the Fano effect. These results will be helpful for understanding the quantum interference in the MBS-assisted Andreev reflection.
Liu, Bin; Li, Yunyun; Zhou, Jun; Nakayama, Tsuneyoshi; Li, Baowen
2016-06-01
We theoretically investigate the spin-dependent Seebeck effect in an Aharonov-Bohm mesoscopic ring in the presence of both Rashba and Dresselhaus spin-orbit interactions under magnetic flux perpendicular to the ring. We apply the Green's function method to calculate the spin Seebeck coefficient employing the tight-binding Hamiltonian. It is found that the spin Seebeck coefficient is proportional to the slope of the energy-dependent transmission coefficients. We study the strong dependence of spin Seebeck coefficient on the Fermi energy, magnetic flux, strength of spin-orbit coupling, and temperature. Maximum spin Seebeck coefficients can be obtained when the strengths of Rashba and Dresselhaus spin-orbit couplings are slightly different. The spin Seebeck coefficient can be reduced by increasing temperature and disorder.
Aharonov-Bohm phase for an electromagnetic wave background
Bright, Max; Yoshida, Atsushi
2015-01-01
The canonical Aharonov-Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov-Bohm phase acquired by a charged particle moving in {\\it time-dependent} potentials . In particular, we focus on the case of a charged particle moving in the time varying field of a plane electromagnetic wave. We work out the Aharonov-Bohm phase using both the potential ({\\it i.e.} $\\oint A_\\mu dx ^\\mu$) and field ({\\it i.e.} $\\frac{1}{2}\\int F_{\\mu \
Characterisation of ferromagnetic rings for Zernike phase plates using the Aharonov-Bohm effect.
Edgcombe, C J; Ionescu, A; Loudon, J C; Blackburn, A M; Kurebayashi, H; Barnes, C H W
2012-09-01
Holographic measurements on magnetised thin-film cobalt rings have demonstrated both onion and vortex states of magnetisation. For a ring in the vortex state, the difference between phases of electron paths that pass through the ring and those that travel outside it was found to agree very well with Aharonov-Bohm theory within measurement error. Thus the magnetic flux in thin-film rings of ferromagnetic material can provide the phase shift required for phase plates in transmission electron microscopy. When a ring of this type is used as a phase plate, scattered electrons will be intercepted over a radial range similar to the ring width. A cobalt ring of thickness 20 nm can produce a phase difference of π/2 from a width of just under 30 nm, suggesting that the range of radial interception for this type of phase plate can be correspondingly small. PMID:22842114
Polarized excitons in nanorings and the optical Aharonov-Bohm effect
Govorov, A. O.; Ulloa, S. E.; Karrai, K.; Warburton, R. J.
2002-08-01
The quantum nature of matter lies in the wave function phases that accumulate while particles move along their trajectories. A prominent example is the Aharonov-Bohm phase, which has been studied in connection with the conductance of nanostructures. However, optical response in solids is determined by neutral excitations, for which no sensitivity to magnetic flux would be expected. We propose a mechanism for the topological phase of a neutral particle, a polarized exciton confined to a semiconductor quantum ring. We predict that this magnetic-field induced phase may strongly affect excitons in a system with cylindrical symmetry, resulting in switching between ``bright'' exciton ground states and novel ``dark'' states with nearly infinite lifetimes. Since excitons determine the optical response of semiconductors, the predicted phase can be used to tailor photon emission from quantum nanostructures.
The second-order Zeeman effect of the sodium clock transition in a weak magnetic field of less than 50 μT was measured as the scalar Aharonov-Bohm phase by two-photon stimulated Raman atom interferometry. The ac Stark effect of the Raman pulse was canceled out by adopting an appropriate intensity ratio of two photons in the Raman pulse. The Ramsey fringes for the pulse separation of 7 ms were obtained with a phase uncertainty of π/200 rad. The nondispersive feature of the scalar Aharonov-Bohm phase was clearly demonstrated through 18 fringes with constant amplitude. The Breit-Rabi formula of the sodium clock transition was verified to be Δν=(0.222±0.003)x1012xB1.998±0.004 in a magnetic field of less than 50 μT.
E. V. B. Leite
2015-01-01
Full Text Available Based on the Kaluza-Klein theory, we study the Aharonov-Bohm effect for bound states for a relativistic scalar particle subject to a Coulomb-type potential. We introduce this scalar potential as a modification of the mass term of the Klein-Gordon equation, and a magnetic flux through the line element of the Minkowski spacetime in five dimensions. Then, we obtain the relativistic bound states solutions and calculate the persistent currents.
Aharonov-Bohm oscillations of a tunable quantum ring
Keyser, U.F; Borck, S.; Haug, R. J.; Wegscheider, W.; Bichler, M.; Abstreiter, G.
2002-01-01
With an atomic force microscope a ring geometry with self-aligned in-plane gates was directly written into a GaAs/AlGaAs-heterostructure. Transport measurements in the open regime show only one transmitting mode and Aharonov-Bohm oscillations with more than 50% modulation are observed in the conductance. The tuning via in-plane gates allows to study the Aharonov-Bohm effect in the whole range from the open ring to the Coulomb-blockade regime.
Jones-Smith, Katherine; Vachaspati, Tanmay
2009-01-01
A solenoid oscillating in vacuum will pair produce charged particles due to the Aharonov-Bohm (AB) interaction. We calculate the radiation pattern and power emitted for charged scalar particles. We extend the solenoid analysis to cosmic strings, and find enhanced radiation from cusps and kinks on loops. We argue by analogy with the electromagnetic AB interaction that cosmic strings should emit photons due to the gravitational AB interaction of fields in the conical spacetime of a cosmic string. We calculate the emission from a kink and find that it is of similar order as emission from a cusp, but kinks are vastly more numerous than cusps and may provide a more interesting observational signature.
Aharonov-Bohm scattering on a cone
Alvarez, Marcos
1998-01-01
The Aharonov-Bohm scattering amplitude is calculated in the context of planar gravity with localized sources which also carry a magnetic flux. These sources cause space-time to develop conical singularities at their location, thus introducing novel effects in the scattering of electrically charged particles. The behaviour of the wave function in the proximity of the classical scattering directions is analyzed by means of an asymptotic expansion previously introduced by the author. It is found...
M. Maamache; C. Lahoulou; Y. Saadi
2009-01-01
Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm effect (AB) and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ(r - R). Consequently, the problem becomes more complicated. In order to avoid this difficulty, we replace the radius R by p(t)R, where p(t) is a positive time-dependent function. Then at the end of calculations we take the limit R →0.The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by p(t), i.e., C > 0, C = 0, and C 0) or continuous (C≤0).
Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm effect (AB) and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ(r - R). Consequently, the problem becomes more complicated. In order to avoid this difficulty, we replace the radius R by ρ(t)R, where ρ(t) is a positive time-dependent function. Then at the end of calculations we take the limit R → 0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by ρ(t), i.e., C > 0, C = 0, and C 0) or continuous (C ≤ 0). (general)
Grochol, Michal; Zimmermann, Roland
2007-01-01
Transition energies and oscillator strengths of excitons in dependence on magnetic field are investigated in type I and II semiconductor nanorings. A slight deviation from circular (concentric) shape of the type II nanoring gives a better observability of the Aharonov-Bohm oscillations since the ground state is always optically active. Kinetic equations for the exciton occupation are solved with acoustic phonon scattering as the major relaxation process, and absorption and luminescence spectr...
Anomalous aharonov-bohm gap oscillations in carbon nanotubes.
Sangalli, Davide; Marini, Andrea
2011-10-12
The gap oscillations caused by a magnetic flux penetrating a carbon nanotube represent one of the most spectacular observations of the Aharonov-Bohm effect at the nanoscale. Our understanding of this effect is, however, based on the assumption that the electrons are strictly confined on the tube surface, on trajectories that are not modified by curvature effects. Using an ab initio approach based on density functional theory, we show that this assumption fails at the nanoscale inducing important corrections to the physics of the Aharonov-Bohm effect. Curvature effects and electronic density that is spilled out of the nanotube surface are shown to break the periodicity of the gap oscillations. We predict the key phenomenological features of this anomalous Aharonov-Bohm effect in semiconductive and metallic tubes and the existence of a large metallic phase in the low flux regime of multiwalled nanotubes, also suggesting possible experiments to validate our results. PMID:21805987
Quantum Computation with Aharonov-Bohm Qubits
Barone, A.; Hakioglu, T.; Kulik, I. O.
2002-01-01
We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum $\\hbar c/e$ as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the doubl...
Grochol, Michal; Zimmermann, Roland
2007-11-01
Transition energies and oscillator strengths of excitons in dependence on magnetic field are investigated in types I and II semiconductor nanorings. A slight deviation from circular (concentric) shape of the type II nanoring gives a better observability of the Aharonov-Bohm oscillations since the ground state is always optically active. Kinetic equations for the exciton occupation are solved with acoustic phonon scattering as the major relaxation process, and absorption and luminescence spectra are calculated, showing deviations from equilibrium. The presence of a nonradiative exciton decay leads to a quenching of the integrated photoluminescence with magnetic field.
Lorentz violation correction to the Aharonov-Bohm scattering
Anacleto, M. A.
2015-10-01
In this paper, using a (2 +1 )-dimensional field theory approach, we study the Aharonov-Bohm (AB) scattering with Lorentz symmetry breaking. We obtain the modified scattering amplitude to the AB effect due to the small Lorentz violation correction in the breaking parameter and prove that up to one loop the model is free from ultraviolet divergences.
Lorentz violation correction to the Aharonov-Bohm scattering
Anacleto, M A
2015-01-01
In this paper, using a (2+1)-dimensional field theory approach we study the Aharonov-Bohm (AB) scattering with Lorentz symmetry breaking. We obtain the modified scattering amplitude to the AB effect due to the small Lorentz violation correction in breaking parameter and prove that up to one-loop the model is free from ultraviolet divergences.
Group-theoretical derivation of Aharonov-Bohm phase shifts
Hagen, C. R. [Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627-0171 (United States)
2013-02-15
The phase shifts of the Aharonov-Bohm effect are generally determined by means of the partial wave decomposition of the underlying Schroedinger equation. It is shown here that they readily emerge from an o(2,1) calculation of the energy levels employing an added harmonic oscillator potential which discretizes the spectrum.
Aharonov-Bohm effect in undoped graphene: Magnetotransport via evanescent waves
Katsnelson, M. I.
2009-01-01
Using conformal mapping technique, compact and general analytic expressions for the effects of magnetic fluxes on conductance and Fano factor of undoped graphene nanoflakes in pseudodiffusive regime are derived.
Aharonov-Bohm phases and Dynamical Casimir Effect in a quantum LC circuit
Yao, Yuan
2016-01-01
We study novel types of contributions to the partition function of the Maxwell system defined on a small compact manifold ${\\mathbb{M}}$ with nontrivial mappings $\\pi_1[U(1)]\\cong\\mathbb{Z}$. These novel contributions cannot be described in terms of conventional physical propagating photons with two transverse polarizations, and instead emerge as a result of tunneling transitions between topologically different but physically identical vacuum winding states. These new terms give an extra contribution to the Casimir pressure, yet to be measured. We argue that if the same system is considered in the background of a small external time-dependent E\\&M field, then real physical photons will be emitted from the vacuum, similar to the dynamical Casimir effect (DCE) where photons are radiated from the vacuum due to time-dependent boundary conditions. We propose an experimental realization of such small effects using a microwave cavity. We also comment on the possible cosmological implications of this effect.
Topological damping of Aharonov-Bohm effect: quantum graphs and vertex conditions
Kurasov, P.; Serio, A
2015-01-01
The magnetic Schro¨dinger operator was studied on a figure 8-shaped graph. It is shown that for specially chosen vertex conditions, the spectrum of the magnetic operator is independent of the flux through one of the loops, provided the flux through the other loop is zero. Topological reasons for this effect are explained.
Electronic energy levels of nanorings with impurities and Aharonov-Bohm effects
Ramírez, S.
2011-10-01
By modeling impurities along a nanoring as general potential forms the Schrödinger equation for ballistic electrons is shown to separate in cylindrical coordinates. We find an analytical eigenvalue equation for N delta-function-barrier impurities in the presence of magnetic flux. Previous calculations of the electronic states of a one-dimensional (1D) and two-dimensional (2D) nanoring for only one or two impurities modeled by equal square barriers is explicitly extended to three and four different or equal impurities modeled as delta-barrier, square-barrier, or delta-well potential forms. This is shown to be generalizable to any number N. Effects on the energy spectra due to magnetic flux and different kinds and numbers of impurities are compared in 1D and 2D nanorings.
Gangopadhyay, Sunandan
2014-01-01
The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a particle moving in the noncommutative plane and in the presence of a magnetic field and an arbitrary potential. Using this action, the equation of motion and the energy spectrum for the partcle are obtained explicitly. The Aharonov-Bohm phase is derived using a variety of methods and several dualities between this system and other commutative and noncommutative systems are demonstrated. Finally, the equivalence of the path integral formulation with the noncommutative Schr\\"{o}dinger equation is also established.
Roshanzamir-Nikou, M.; Goudarzi, H.
2016-02-01
A strong magnetic field significantly affects the intrinsic magnetic moment of fermions. In quantum electrodynamics, it was shown that the anomalous magnetic moment of an electron arises kinematically, while it results from a dynamical interaction with an external magnetic field for hadrons (proton). Taking the anomalous magnetic moment of a fermion into account, we find an exact expression for the boundstate energy and the corresponding eigenfunctions of a two-dimensional nonrelativistic spin-1/2 harmonic oscillator with a centripetal barrier (known as the isotonic oscillator) including an Aharonov-Bohm term in the presence of a strong magnetic field. We use the Laplace transform method in the calculations. We find that the singular solution contributes to the phase of the wave function at the origin and the phase depends on the spin and magnetic flux.
The Aharonov-Bohm-Casher ring-dot as a flux-tunable resonant tunneling diode
Citro, R; Romeo, F.
2008-01-01
A mesoscopic ring subject to the Rashba spin-orbit interaction and sequentially coupled to an interacting quantum dot, in the presence of Aharonov-Bohm flux, is proposed as a flux tunable tunneling diode. The analysis of the conductance by means of the nonequilibrium Green's function technique, shows an intrinsic bistability at varying the Aharonov-Bohm flux when 2U > \\pi \\Gamma, U being the charging energy on the dot and \\Gamma the effective resonance width. The bistability properties are di...
Relativistic scalar Aharonov-Bohm scattering
Full text follows: We study the scattering of a charged spin zero relativistic particle from a fixed, thin, infinitely long solenoid in the framework of the first quantization comparing with the results obtained using the field theory approach. The scattering amplitude, within the viewpoint of the relativistic quantum mechanics, can be calculated exactly as a mimic of the nonrelativistic case, either in the original Aharonov-Bohm way or by using the Berry's magnetization scheme. To implement the perturbative analysis within the first-quantized treatment, we consider the Feshbach-Villars two-component formalism of the Klein-Gordon equation. It is shown that the first Born approximation gives an incomplete result while the second order is divergent as occurs in the nonrelativistic counterpart. We search for additional interactions which might provide the appropriated renormalization of the amplitude. It is shown that the addition of a phenomenological magnetic interaction (naively inspired in the spin half case) generates the correct first order term in the the nonrelativistic leading order but it does not give reasonable results in higher orders. We demonstrate that an external delta potential is necessary to reproduce the correct perturbation expansion as happens in the nonrelativistic situation. However, it does not produce the same effect of the quartic self-interaction in the second quantized treatment, which corresponds to the two body sector of a scalar Chern-Simons theory. In the later case, additional contributions coming from vacuum polarization and vertex corrections spoil the scale invariance characteristic of the nonrelativistic Aharonov-Bohm scattering. (author)
Realization of adiabatic Aharonov-Bohm scattering with neutrons
Sjöqvist, Erik; Almquist, Martin; Mattsson, Ken; Gürkan, Zeynep Nilhan; Hessmo, Björn
2015-11-01
The adiabatic Aharonov-Bohm (AB) effect is a manifestation of the Berry phase acquired when some slow variables take a planar spin around a loop. While the effect has been observed in molecular spectroscopy, direct measurement of the topological phase shift in a scattering experiment has been elusive in the past. Here, we demonstrate an adiabatic AB effect by explicit simulation of the dynamics of unpolarized very slow neutrons that scatter on a long straight current-carrying wire.
Kondo, Kenji
2016-01-01
Many researchers have reported on spin filters using linear Rashba spin-orbit interactions (SOI). However, spin filters using square and cubic Rashba SOIs have not yet been reported. We consider that this is because the Aharonov-Casher (AC) phases acquired under square and cubic Rashba SOIs are ambiguous. In this study, we try to derive the AC phases acquired under square and cubic Rashba SOIs from the viewpoint of non-Abelian SU(2) gauge theory. These AC phases can be derived successfully from the non-Abelian SU(2) gauge theory without the completing square methods. Using the results, we investigate the spin filtering in a double quantum dot (QD) Aharonov-Bohm (AB) ring under linear, square, and cubic Rashba SOIs. This AB ring consists of elongated QDs and quasi-one-dimensional quantum nanowires under an external magnetic field. The spin transport is investigated from the left nanowire to the right nanowire in the above structure within the tight-binding approximation. In particular, we focus on the difference of spin filtering among linear, square, and cubic Rashba SOIs. The calculation is performed for the spin polarization by changing the penetrating magnetic flux for the AB ring subject to linear, square, and cubic Rashba SOIs. It is found that perfect spin filtering is achieved for all of the Rashba SOIs. This result indicates that this AB ring under general Rashba SOIs can be a promising device for spin current generation. Moreover, the AB rings under general Rashba SOIs behave in totally different ways in response to penetrating magnetic flux, which is attributed to linear, square, and cubic behaviors in the in-plane momentum. This result enables us to make a clear distinction between linear, square, and cubic Rashba SOIs according to the peak position of the perfect spin filtering.
Magnetic edge states in Aharonov-Bohm graphene quantum rings
Farghadan, R.; Saffarzadeh, A.; Semiromi, E. Heidari
2014-01-01
The effect of electron-electron interaction on the electronic structure of Aharonov-Bohm (AB) graphene quantum rings (GQRs) is explored theoretically using the single-band tight-binding Hamiltonian and the mean-field Hubbard model. The electronic states and magnetic properties of hexagonal, triangular and circular GQRs with different sizes and zigzag edge terminations are studied. The results show that, although the AB oscillations in the all types of nanoring are affected by the interaction,...
Chiao, R Y; Sundqvist, K M; Inan, N A; Munoz, G A; Singleton, D A; Kang, B S; Martinez, L A
2014-01-01
In this paper we investigate the scalar Aharonov-Bohm (AB) effect in two of its forms, i.e., its electric form and its gravitational form. The standard form of the electric AB effect involves having particles (such as electrons) move in regions with zero electric field but different electric potentials. When a particle is recombined with itself, it will have a different phase, which can show up as a change in the way the single particle interferes with itself when it is recombined with itself. In the case where one has quasi-static fields and potentials, the particle will invariably encounter fringing fields, which makes the theoretical and experimental status of the electric AB effect much less clear than that of the magnetic (or vector) AB effect. Here we propose using time varying fields outside of a spherical shell, and potentials inside a spherical shell to experimentally test the scalar AB effect. In our proposal a quantum system will always be in a field-free region but subjected to a non-zero time-var...
Maamache, M.; Lahoulou, C.; Saadi, Y.
2009-05-01
Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm effect (AB) and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ(r - R). Consequently, the problem becomes more complicated. In order to avoid this difficulty, we replace the radius R by ρ(t)R, where ρ(t) is a positive time-dependent function. Then at the end of calculations we take the limit R → 0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by ρ(t), i.e., C > 0, C = 0, and C 0) or continuous (C <= 0).
Chiao, Raymond
2012-01-01
A novel kind of nonlocal, macroscopic Aharonov-Bohm effect involving two topologically linked superconducting rings made out of two different materials, namely, lead and tin, is suggested for experimental observation, in which the lead ring is a torus containing a core composed of permanently magnetized ferromagnetic material. It is predicted that the remnant fields in a hysteresis loop induced by the application of a magnetic field imposed by a large external pair of Helmholtz coils upon the tin ring, will be asymmetric with respect to the origin of the loop. An appendix based on Feynman's path-integral principle is the basis for these predictions.
Kao, W. F.; Kao, Y. M.; Lin, D. H.
2002-01-01
A useful and universal formula for the expectation value of the radial operator in the presence of the Aharonov-Bohm flux and the Coulomb Field is established. We find that the expectation value $$ $(-\\infty \\leq \\lambda \\leq \\infty)$ is greatly affected due to the non-local effect of the magnetic flux although the Aharonov-Bohm flux does not have any dynamical significance in classical mechanics. In particular, the quantum fluctuation increases in the presence of the magnetic f...
Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
Ferrari, A. F.; Gomes, M; Stechhahn, C. A.
2007-01-01
In this work we study modifications in the Aharonov-Bohm effect for relativistic spin 1/2 particles due to the noncommutativity of spacetime in $2 + 1$ dimensions. The noncommutativity gives rise to a correction to the Aharonov-Bohm potential which is highly singular at the origin, producing divergences in a perturbative expansion around the usual solution of the free Dirac equation. This problem is surmounted by using a perturbative expansion around the exact solution of the \\textit{commutat...
On the Aharonov-Bohm diffusion
The diffusion of a charged particle by a singular flux tube is revisited. A simple and rigourous derivation shows that the action of the propagator on an incident plane wave precisely yields the Aharonov-Bohm diffusion amplitude. The forward diffusion is discussed as well as the singularity of the interaction at the position of the flux tube. (orig.)
Time-dependent Aharonov-Bohm Hamiltonian and admissibility criteria of quantum wave functions
Self-adjointness of the time-independent Aharonov-Bohm Hamiltonians is shown to allow a continuous family of different dynamics including those following from Pauli's criterion of rotational invariance, Aharonov-Bohm criterion of single valuedness and a version of Pauli's criterion appropriate to cylindrical symmetry suggested by Henneberger. A time-dependent flux F(t) linking the Aharonov-Bohm solenoid leads to the time-dependent AB Hamiltonian. Explicit solutions in cases with and without inaccessible regions for the charged particle rule out applicability of both versions of the Pauli criterion. The solutions contain one time-independent parameter α, integer values of which correspond to single-valued wave functions. Any real (integer or noninteger) value of α is allowed. Charge and current densities depend on α and F(t) only through the combination changing the flux during an experiment can be understood as local effects of the electric field inevitably associated with changing magnetic flux
Aharonov-Bohm detection of two-dimensional magnetostatic cloaks
Valagiannopoulos, Constantinos A.; Askarpour, Amir Nader; Alù, Andrea
2015-12-01
Two-dimensional magnetostatic cloaks, even when perfectly designed to mitigate the magnetic field disturbance of a scatterer, may be still detectable with Aharonov-Bohm (AB) measurements, and therefore may affect quantum interactions and experiments with elongated objects. We explore a multilayered cylindrical cloak whose permeability profile is tailored to nullify the magnetic-flux perturbation of the system, neutralizing its effect on AB measurements, and simultaneously optimally suppress the overall scattering. In this way, our improved magnetostatic cloak combines substantial mitigation of the magnetostatic scattering response with zero detectability by AB experiments.
Hidden Photons in Aharonov-Bohm-Type Experiments
Arias, Paola; Diaz, Marco Aurelio; Jaeckel, Joerg; Koch, Benjamin; Redondo, Javier
2016-01-01
We discuss the Aharonov-Bohm effect in the presence of hidden photons kinetically mixed with the ordinary electromagnetic photons. The hidden photon field causes a slight phase shift in the observable interference pattern. It is then shown how the limited sensitivity of this experiment can be largely improved. The key observation is that the hidden photon field causes a leakage of the ordinary magnetic field into the supposedly field-free region. The direct measurement of this magnetic field can provide a sensitive experiment with a good discovery potential, particularly below the $\\sim$ meV mass range for hidden photons.
Patterns of the Aharonov-Bohm oscillations in graphene nanorings
Romanovsky, Igor; Yannouleas, Constantine; Landman, Uzi
2012-01-01
Using extensive tight-binding calculations, we investigate (including the spin) the Aharonov-Bohm (AB) effect in monolayer and bilayer trigonal and hexagonal graphene rings with zigzag boundary conditions. Unlike the previous literature, we demonstrate the universality of integer (hc/e) and half-integer (hc/2e) values for the period of the AB oscillations as a function of the magnetic flux, in consonance with the case of mesoscopic metal rings. Odd-even (in the number of Dirac electrons, N) s...
Hidden superconformal symmetry of the spinless Aharonov-Bohm system
A hidden supersymmetry is revealed in the spinless Aharonov-Bohm problem. The intrinsic supersymmetric structure is shown to be intimately related to the scale symmetry. As a result, a bosonized superconformal symmetry is identified in the system. Different self-adjoint extensions of the Aharonov-Bohm problem are studied in the light of this superconformal structure and interacting anyons. The scattering problem of the original Aharonov-Bohm model is discussed in the context of the revealed supersymmetry.
Hidden superconformal symmetry of spinless Aharonov-Bohm system
Correa, Francisco; Falomir, Horacio; Jakubsky, Vit; Plyushchay, Mikhail S.
2009-01-01
A hidden supersymmetry is revealed in the spinless Aharonov-Bohm problem. The intrinsic supersymmetric structure is shown to be intimately related with the scale symmetry. As a result, a bosonized superconformal symmetry is identified in the system. Different self-adjoint extensions of the Aharonov-Bohm problem are studied in the light of this superconformal structure and interacting anyons. Scattering problem of the original Aharonov-Bohm model is discussed in the context of the revealed sup...
Effect of the Aharonov - Bohm Flux on the Magnetic Gap Soliton%一维铁磁链中的磁隙孤子激发
许长谭
2001-01-01
采用Holstein-Primakoff变换、相干态表示、含时微扰原理和多重标度方法,研究了Aharonov-Bohm(A-B)磁通对一维铁磁链中的磁隙孤子产生的影响,得到了在A-B磁通影响下的磁隙孤子的峰值、宽度、能量和自旋空间排列.
Aharonov--Bohm problem for vector bosons
Castro, Luis B
2015-01-01
The Aharonov--Bohm (AB) problem for vector bosons by the Duffin--Kemmer--Petiau (DKP) formalism is analyzed. The relevant eigenvalue equation coming from the DKP formalism reveals an equivalence to the spin--$1/2$ AB problem. By using the self--adjoint extension approach, we examine the bound state scenario. The energy spectra are explicitly computed as well as their dependencies on the magnetic flux parameter and also the conditions for the occurrence of bound states.
Propagator for an Aharonov-Bohm-Coulomb system
Park, D. K.; Yoo, Sahng-Kyoon; Lee, Soo-Young; Kahng, Jae-Rok; Park, Chang Soo; Yim, Eui-Soon; Lee, C.H.
1997-01-01
The propagator of three-dimensional Aharonov-Bohm-Coulomb system is calculated by following the Duru-Kleinert method. It is shown that the system is reduced to two independent two dimensional Aharonov-Bohm plus harmonic oscillator systems through dimensional extension and Kustaanheimo-Stiefel transformation. The energy spectrum is deduced.
Ji, Haojie
In this thesis I develop understanding of the fundamental physical and material properties of type-II ZnTe/ZnSe submonolayer quantum dots (QDs), grown via combination of molecular beam epitaxy (MBE) and migration enhanced epitaxy (MEE). I use magneto-photoluminescence, including excitonic Aharonov-Bohm (AB) effect and polarized optical spectroscopy as the primary tools in this work. I present previous studies as well as the background of optical and magneto-optical processes in semiconductor nanostructures and introduce the experimental methods in Chapters 1 - 3. In Chapter 4 I focus on the excitonic AB effect in the type-II QDs. I develop a lateral tightly-bound exciton model for ZnTe/ZnSe type-II QDs, using analytical methods and numerical calculations. This explained the magneto-PL observation and allowed for establishing the size and density of the QDs in each sample based on the results of PL and magneto-PL measurements. For samples with larger QDs, I observe behaviors that fall between properties of quantum-dot and quantum-well-like systems due to increased QD densities and their type-II nature. Finally, the decoherence mechanisms of the AB excitons are investigated via the temperature dependent studies of the magneto-PL. It is determined that the AB exciton decoherence is due to transport-like (acoustic phonon) scattering of the electrons moving in the ZnSe barriers, but with substantially smaller magnitude of electron-phonon coupling constant due to relatively strong electron-hole coupling within these type-II QDs. In Chapter 5 I discuss the results of circularly polarized magneto-PL measurements. A model with ultra-long spin-flip time of holes confined to submonolayer QDs is proposed. The g-factor of type-II excitons was extracted from the Zeeman splitting and the g-factor of electrons was obtained by fitting the temperature dependence of the degree of circular polarization (DCP), from which g-factor of holes confined within ZnTe QDs was found. It is shown
Using nonequilibrium Green's function techniques, we investigate Andreev reflection and Aharonov-Bohm oscillations through a parallel-coupled double quantum dot connected with a ferromagnetic lead and a superconductor lead. The possibility of controlling Andreev reflection and Aharonov-Bohm oscillations of the system is explored by tuning the interdot coupling, the gate voltage, the magnetic flux, and the intradot spin-flip scattering. When the spin-flip scattering increases, Fano resonant peaks resulting from the asymmetrical levels of the two quantum dots begin to split, and Aharonov-Bohm oscillations are suppressed. Due to the interdot coupling, one strongly and one weakly coupled state of the system can be formed. The magnetic flux can exchange the function of the two states, which leads to a swap effect.
Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
In this work we study modifications in the Aharonov-Bohm effect for relativistic spin 1/2 particles due to the noncommutativity of spacetime in 2+1 dimensions. The noncommutativity gives rise to a correction to the Aharonov-Bohm potential which is highly singular at the origin, producing divergences in a perturbative expansion around the usual solution of the free Dirac equation. This problem is surmounted by using a perturbative expansion around the exact solution of the commutative Aharonov-Bohm problem. We calculate, in this setting, the scattering amplitude and the corrections to the differential and total cross sections for a spin 1/2 particle, in the small-flux limit
Vaidman, Lev; Dennis, Mark; Popescu, Sandu
2010-01-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to the subject of quantum phases and highlighting the impact of the discovery of the Aharonov--Bohm effect and of the Berry phase across physics. Researchers working in the area are invited to submit papers of original research to this issue. Editorial policy The Editorial Board has invited Lev Vaidman, Mark Dennis and Sandu Popescu to serve as Guest Editors for the special issue. The criteria for acceptance of contributions are as follows: Contributions will be refereed and processed according to the usual procedure and high standards of the journal. Papers should be original and should contain substantial new results. All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The DEADLINE for contributed papers will be 1 February 2010. This deadline will allow the special issue to appear in September 2010. Advice on publishing your work in Journal of Physics A: Mathematical and Theoretical www.iop.org/Journals/jphysa. Contributions to the special issue should be submitted electronically, if possible, by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'JPhysA Special Issue— Quantum Phases'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, IOP Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. Please quote 'JPhysA Special Issue— Quantum Phases'. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any
Magnetic edge states in Aharonov-Bohm graphene quantum rings
Farghadan, R., E-mail: rfarghadan@kashanu.ac.ir; Heidari Semiromi, E. [Department of Physics, University of Kashan, Kashan (Iran, Islamic Republic of); Saffarzadeh, A. [Department of Physics, Payame Noor University, P.O. Box 19395-3697 Tehran (Iran, Islamic Republic of); Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6 (Canada)
2013-12-07
The effect of electron-electron interaction on the electronic structure of Aharonov-Bohm (AB) graphene quantum rings (GQRs) is explored theoretically using the single-band tight-binding Hamiltonian and the mean-field Hubbard model. The electronic states and magnetic properties of hexagonal, triangular, and circular GQRs with different sizes and zigzag edge terminations are studied. The results show that, although the AB oscillations in the all types of nanoring are affected by the interaction, the spin splitting in the AB oscillations strongly depends on the geometry and the size of graphene nanorings. We found that the total spin of hexagonal and circular rings is zero and therefore, no spin splitting can be observed in the AB oscillations. However, the non-zero magnetization of the triangular rings breaks the degeneracy between spin-up and spin-down electrons, which produces spin-polarized AB oscillations.
Patterns of the Aharonov-Bohm oscillations in graphene nanorings
Romanovsky, Igor; Yannouleas, Constantine; Landman, Uzi
2012-04-01
Using extensive tight-binding calculations, we investigate (including the spin) the Aharonov-Bohm (AB) effect in monolayer and bilayer trigonal and hexagonal graphene rings with zigzag boundary conditions. Unlike the previous literature, we demonstrate the universality of integer (hc/e) and half-integer (hc/2e) values for the period of the AB oscillations as a function of the magnetic flux, in consonance with the case of mesoscopic metal rings. Odd-even (in the number of Dirac electrons, N) sawtooth-type patterns relating to the halving of the period have also been found; they are more numerous for a monolayer hexagonal ring, compared to the cases of a trigonal and a bilayer hexagonal ring. Additional, more complicated patterns are also present, depending on the shape of the graphene ring. Overall, the AB patterns repeat themselves as a function of N, with periods proportional to the number of the sides of the rings.
Magnetic edge states in Aharonov-Bohm graphene quantum rings
Farghadan, R.; Saffarzadeh, A.; Heidari Semiromi, E.
2013-12-01
The effect of electron-electron interaction on the electronic structure of Aharonov-Bohm (AB) graphene quantum rings (GQRs) is explored theoretically using the single-band tight-binding Hamiltonian and the mean-field Hubbard model. The electronic states and magnetic properties of hexagonal, triangular, and circular GQRs with different sizes and zigzag edge terminations are studied. The results show that, although the AB oscillations in the all types of nanoring are affected by the interaction, the spin splitting in the AB oscillations strongly depends on the geometry and the size of graphene nanorings. We found that the total spin of hexagonal and circular rings is zero and therefore, no spin splitting can be observed in the AB oscillations. However, the non-zero magnetization of the triangular rings breaks the degeneracy between spin-up and spin-down electrons, which produces spin-polarized AB oscillations.
Magnetic edge states in Aharonov-Bohm graphene quantum rings
The effect of electron-electron interaction on the electronic structure of Aharonov-Bohm (AB) graphene quantum rings (GQRs) is explored theoretically using the single-band tight-binding Hamiltonian and the mean-field Hubbard model. The electronic states and magnetic properties of hexagonal, triangular, and circular GQRs with different sizes and zigzag edge terminations are studied. The results show that, although the AB oscillations in the all types of nanoring are affected by the interaction, the spin splitting in the AB oscillations strongly depends on the geometry and the size of graphene nanorings. We found that the total spin of hexagonal and circular rings is zero and therefore, no spin splitting can be observed in the AB oscillations. However, the non-zero magnetization of the triangular rings breaks the degeneracy between spin-up and spin-down electrons, which produces spin-polarized AB oscillations
New formulae for the Aharonov-Bohm wave operators
Richard, Serge
2008-01-01
It is proved that the wave operators corresponding to Schr¨odinger operators with Aharonov- Bohm type magnetic fields can be rewritten in terms of explicit functions of the generator of dilations and of the Laplacian.
Unitarity of the Aharonov-Bohm Scattering Amplitudes
Arai, Masato; Minakata, Hisakazu
1996-01-01
We discuss the unitarity relation of the Aharonov-Bohm scattering amplitude with the hope that it distinguishes between the differing treatments which employ different incident waves. We find that the original Aharonov-Bohm scattering amplitude satisfies the unitarity relation under the regularization prescription whose theoretical foundation does not appear to be understood. On the other hand, the amplitude obtained by Ruijsenaars who uses plane wave as incident wave also satisfies the unita...
Mesoscopic Persistent Currents, Aharonov-Bohm Magnetic Flux and Time Reversal Symmetry
LI Hua-Zhong
2003-01-01
We discuss the effect of Aharonov-Bohm magnetic flux on the time reversal symmetric properties of .mesoscopic metallic ring systems. It is usually believed that AB flux causes time reversal symmetry breaking. We analyse the case of mesoscopic persistent currents and find out that AB flux does not breai time reversal symmetry. Our arguments are supported by the general theory of mesoscopic persistent currents.
Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfest's theorem
The electron diffraction pattern for two-slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern which is asymmetric but with a symmetric envelope. In general, both expected displacement and kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless Ehrenfest's theorems and the conservation of momentum are satisfied. (author)
Axial anomaly in the presence of the Aharonov-Bohm gauge field
The axial anomaly for Euclidean Dirac fermions in the presence of a background Aharonov-Bohm gauge potential was computed. The non-perturbative result depends on the self-adjoint extensions of the Dirac operator. The role of the quantum mechanical parameters involved in the expression for the axial anomaly is discussed. A derivation of the effective action by means of the stereographic projection is also considered. (authors). 14 refs
Aharonov-Bohm phases in a quantum LC circuit
Cao, ChunJun; Yao, Yuan; Zhitnitsky, Ariel R.
2016-03-01
We study novel types of contributions to the partition function of the Maxwell system defined on a small compact manifold. These contributions, often not addressed in the perturbative treatment with physical photons, emerge as a result of tunneling transitions between topologically distinct but physically identical vacuum winding states. These new terms give an extra contribution to the Casimir pressure, yet to be measured. We argue that this effect is highly sensitive to a small external electric field, which should be contrasted with the conventional Casimir effect, where the vacuum photons are essentially unaffected by any external field. Furthermore, photons will be emitted from the vacuum in response to a time-dependent electric field, similar to the dynamical Casimir effect in which real particles are radiated from the vacuum due to the time-dependent boundary conditions. We also propose an experimental setup using a quantum LC circuit to detect this novel effect. We expect physical electric charges to appear on the capacitor plates when the system dimension is such that coherent Aharonov-Bohm phases can be maintained over macroscopically large distances.
Quantum interference and Aharonov-Bohm oscillations in topological insulators.
Bardarson, Jens H; Moore, Joel E
2013-05-01
Topological insulators (TIs) have an insulating bulk but a metallic surface. In the simplest case, the surface electronic structure of a three-dimensional (3D) TI is described by a single two-dimensional (2D) Dirac cone. A single 2D Dirac fermion cannot be realized in an isolated 2D system with time-reversal symmetry, but rather owes its existence to the topological properties of the 3D bulk wavefunctions. The transport properties of such a surface state are of considerable current interest; they have some similarities with graphene, which also realizes Dirac fermions, but have several unique features in their response to magnetic fields. In this review we give an overview of some of the main quantum transport properties of TI surfaces. We focus on the efforts to use quantum interference phenomena, such as weak anti-localization and the Aharonov-Bohm effect, to verify in a transport experiment the Dirac nature of the surface state and its defining properties. In addition to explaining the basic ideas and predictions of the theory, we provide a survey of recent experimental work. PMID:23552181
Aharonov-Bohm oscillation modes in double-barrier nanorings
Zhu, Jia-Lin; Yu, Xiquan; Dai, Zhensheng; Hu, Xiao
2003-02-01
The energy spectrum and Aharonov-Bohm (AB) effect in a two-dimensional nanoring interrupted by two identical barriers are studied, and a way of labeling a state according to the node numbers of the wave function in the absence of magnetic flux is introduced. It is found that a magnetic flux φ can modify both the phase and amplitude of wave functions due to the presence of the barriers. AB oscillations are strongly affected by the double barriers, and there are two modes of strong AB oscillations, named O and X modes. The energy levels of O and X modes are occasionally degenerate at φ=0 and 0.5, respectively, and the corresponding wave functions of both degenerate states are localized and can be greatly modified by a small change of φ. The O mode of AB oscillations, which does not exist in the parallel double-barrier ring usually used in experiments, presents an interesting picture and suggests other related phenomena.
Aharonov-Bohm oscillation modes in double-barrier nanorings
The energy spectrum and Aharonov-Bohm (AB) effect in a two-dimensional nanoring interrupted by two identical barriers are studied, and a way of labeling a state according to the node numbers of the wave function in the absence of magnetic flux is introduced. It is found that a magnetic flux φ can modify both the phase and amplitude of wave functions due to the presence of the barriers. AB oscillations are strongly affected by the double barriers, and there are two modes of strong AB oscillations, named O and X modes. The energy levels of O and X modes are occasionally degenerate at φ=0 and 0.5, respectively, and the corresponding wave functions of both degenerate states are localized and can be greatly modified by a small change of φ. The O mode of AB oscillations, which does not exist in the parallel double-barrier ring usually used in experiments, presents an interesting picture and suggests other related phenomena
Fingerprints of Majorana Bound States in Aharonov-Bohm Geometry
Tripathi, Krashna Mohan; Das, Sourin; Rao, Sumathi
2016-04-01
We study a ring geometry, coupled to two normal metallic leads, which has a Majorana bound state (MBS) embedded in one of its arms and is threaded by Aharonov-Bohm (A B ) flux ϕ . We show that by varying the A B flux, the two leads go through resonance in an anticorrelated fashion while the resonance conductance is quantized to 2 e2/h . We further show that such anticorrelation is completely absent when the MBS is replaced by an Andreev bound state (ABS). Hence this anti-correlation in conductance when studied as a function of ϕ provides a unique signature of the MBS which cannot be faked by an ABS. We contrast the phase sensitivity of the MBS and ABS in terms of tunneling conductances. We argue that the relative phase between the tunneling amplitude of the electrons and holes from either lead to the level (MBS or ABS), which is constrained to 0 ,π for the MBS and unconstrained for the ABS, is responsible for this interesting contrast in the A B effect between the MBS and ABS.
Aharonov-Bohm oscillations in singly connected disordered conductors.
Aleiner, I L; Andreev, A V; Vinokur, V
2015-02-20
We show that the transport and thermodynamic properties of a singly connected disordered conductor exhibit quantum Aharonov-Bohm oscillations as a function of the total magnetic flux through the sample. The oscillations are associated with the interference contribution from a special class of electron trajectories confined to the surface of the sample. PMID:25763968
Spectral and scattering theory for the Aharonov-Bohm operators
Pankrashkin, Konstantin; Richard, Serge
2011-01-01
We review the spectral and the scattering theory for the Aharonov-Bohm model on $\\mathbb{R}^2$. New formulae for the wave operators and for the scattering operator are presented. The asymptotics at high and at low energy of the scattering operator are computed.
Putting a Spin on the Aharonov-Bohm Oscillations
Anandan, Jeeva
2002-01-01
An experiment that shows the modulation of the Aharonov-Bohm oscillations of magneto-resistance in a mesoscopic ring is described. Possible theoretical explanations of this modulation due to the interaction of the electron spin with the magnetic and electric fields are considered.
Boyer, Timothy H
2014-01-01
A new classical electromagnetic analysis is presented suggesting that the Aharonov-Bohm phase shift is overwhelmingly likely to arise from a classical lag effect based upon classical electromagnetic forces. The analysis makes use of several aspects of classical electromagnetic theory which are unfamiliar to most physicists, including the Darwin Lagrangian, acceleration-based electric fields, internal electromagnetic momentum in a magnet, and a magnet model involving at least three mutually-interacting particles. Only when the acceleration-based electric forces acting on the passing charge are included do we find consistency with all the relativistic conservation laws: energy, linear momentum, angular momentum, and constant center-of-mass velocity. The electric forces on the passing charge lead to a lag effect which accounts quantitatively for the Aharonov-Bohm phase shift. Thus the classical analysis strongly suggests that the Aharonov-Bohm phase shift (observed when electrons pass a long solenoid which corre...
Gate controlled Aharonov-Bohm-type oscillations from single neutral excitons in quantum rings
Ding, F.; Akopian, N.; Li, B.; Perinetti, U.; Govorov, A.; Peeters, F. M.; Bof Bufon, C. C.; Deneke, C.; Chen, Y. H.; Rastelli, A.; Schmidt, O. G.; Zwiller, V.
2010-08-01
We report on a magnetophotoluminescence study of single self-assembled semiconductor nanorings which are fabricated by molecular-beam epitaxy combined with AsBr3 in situ etching. Oscillations in the neutral exciton radiative recombination energy and in the emission intensity are observed under an applied magnetic field. Further, we control the period of the oscillations with a gate potential that modifies the exciton confinement. We infer from the experimental results, combined with calculations, that the exciton Aharonov-Bohm effect may account for the observed effects.
Zhang, G.; Li, X.Q.(Nankai University, Tianjin, 300071, People's Republic of China); Zhang, X. Z.; Song, Z.
2014-01-01
We study the effect of PT-symmetric imaginary potentials embedded in the two arms of an Aharonov-Bohm interferometer on the transmission phase by finding an exact solution for a concrete tight-binding system. It is observed that the spectral singularity always occurs at k=${\\pm}${\\pi}/2 for a wide range of fluxes and imaginary potentials. Critical behavior associated with the physics of the spectral singularity is also investigated. It is demonstrated that the quasi-spectral singularity corre...
Force-free gravitational redshift: proposed gravitational Aharonov-Bohm experiment.
Hohensee, Michael A; Estey, Brian; Hamilton, Paul; Zeilinger, Anton; Müller, Holger
2012-06-01
We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces. PMID:23003927
Coherent control of interacting particles using dynamical and Aharonov-Bohm phases
Creffield, Charles E.; Platero, G.
2010-01-01
A powerful method of manipulating the dynamics of quantum coherent particles is to control the phase of their tunneling. We consider a system of two electrons hopping on a quasi-one- dimensional lattice in the presence of a uniform magnetic field and study the effect of adding a time-periodic driving potential. We show that the dynamical phases produced by the driving can combine with the Aharonov-Bohm phases to give precise control of the localization and dynamics of the particles, even in t...
Force-free gravitational redshift: a gravitostatic Aharonov-Bohm experiment
Hohensee, Michael A; Hamilton, Paul; Zeilinger, Anton; Mueller, Holger
2011-01-01
We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.
Quantum transport through two series Aharonov-Bohm interferometers with zero total magnetic flux
Wang Jian-Ming; Wang Rui; Zhang Yong-Ping; Liang Jiu-Qing
2007-01-01
With the help of nonequilibrium Green's function technique, the electronic transport through series AharonovBohm (AB) interferometers is investigated. We obtain the AB interference pattern of the transition probability characterized by the algebraic sum φ and the difference θ of two magnetic fluxes, and particularly a general rule of AB oscillation period depending on the ratio of integer quantum numbers of the fluxes. A parity effect is observed, showing the asymmetric AB oscillations with respect to the even and odd quantum numbers of the total flux in antiparallel AB interferometers. It is also shown that the AB flux can shift the Fano resonance peaks of the transmission spectrum.
Electron transport through an Aharonov-Bohm ring with a side-coupled quantum dot
We present a theoretical description for electron transport through an Aharonov-Bohm ring with a quantum dot side-coupled to one arm. An analytic formula of conductance is derived which shows the Aharonov-Bohm oscillations. The quantum dot modulates electron transmission through the coupled arm, and thus affects the amplitude of the AB oscillations. Tuning the plunger gate of the quantum dot can induce the antiresonance, in which the transmission through the coupled arm is quenched and the Aharonov-Bohm oscillations are suppressed completely. The temperature-dependence of the suppression of the Aharonov-Bohm oscillations is discussed
Full text: We study the charge persistent current (PC) in a one dimensional mesoscopic ring pierced by Aharonov-Bohm-Casher fluxes coupled to a side-branch quantum dot with a singly occupied level at Kondo resonance. For privileged values of the fluxes the problem can be mapped onto an integrable model, exactly solvable by a Bethe ansatz. In the case of a pure magnetic Aharonov-Bohm flux, we find - contrary to recent claims in the literature - that the presence of the quantum dot has no effect on the PC. In contrast, the Kondo resonance interferes with the spin-dependent Aharonov-Casher effect to induce a term in the PC that scales as 1/N in the strong coupling regime, with N the number of electrons in the ring