相关论文: Magnetic Force Exerted by the Aharonov-Bohm Line
Consider the scattering amplitude $s(\omega,\omega^\prime;\lambda)$, $\omega,\omega^\prime\in{\Bbb S}^{d-1}$, $\lambda > 0$, corresponding to an arbitrary short-range magnetic field $B(x)$, $x\in{\Bbb R}^d$. This is a smooth function of…
We revisit the problem of a charged particle scattering off of an Aharonov-Bohm cosmic string. A classic computation gave an infinite total scattering cross section, leading to a Callan-Rubakov-like enhancement which can have important…
The problem of the scattering of a charged test particle in the gravitational background of axially symmetrical wormhole in the presence of the Aharonov-Bohm type magnetic field is considered. It is shown that the natural mathematical…
Magnetic Aharonov-Bohm effect (AB effect) was studied in hundreds of papers starting with the seminal paper of Aharonov and Bohm [AB] published in 1959. We give a new proof of the magnetic Aharonov-Bohm effect without using the scattering…
Quantum-mechanical theory for scattering of nonrelativistic charged particles with spin by a penetrable magnetic vortex is elaborated. The scattering differential cross section is shown to consist of two terms, one describing diffraction on…
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…
The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the interaction between two particles carrying electric charge and magnetic flux, say, Chern--Simons solitons, or so called anyons. The scattering problem for such two-body…
It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines…
Partial wave theory of a two dimensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard disk'' like potential and the magnetic flux is…
Mean Field Theory has been extensively used in the study of systems of anyons in two spatial dimensions. In this paper we study the physical grounds for the validity of this approximation by considering the Quantum Mechanical scattering of…
In this paper we review some aspects of the scattering Aharonov-Bohm effect and Berry's phase. Specifically, the problem of scattering of free 2d electrons on the system of an arbitrary number of parallel, infinitely thin and infinitely…
We investigate the scattering of an electron by an infinitely thin and infinitely long straight magnetic flux tube in the framework of QED. We discuss the solutions of the Dirac and Maxwell fields in the related external pure AB potential…
The problem of two Aharonov-Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed in [J. M. Myers, J. Math. Phys. \textbf{6}, 1839 (1963)] for diffraction on a slit can be…
It is shown that the breakdown of a {\it global} symmetry group to a discrete subgroup can lead to analogues of the Aharonov-Bohm effect. At sufficiently low momentum, the cross-section for scattering of a particle with nontrivial $\Z_2$…
We study linear and nonlinear wave scattering by an optical vortex in a self-defocusing nonlinear Kerr medium. In the linear case, we find a splitting of a plane-wave front at the vortex proportional to its circulation, similar to what…
The Aharonov-Bohm (AB) effect was convincingly demonstrated using a micro-sized toroidal magnet but it is almost always explained using an infinitely-long solenoid or an infinitely-long flux line. The main reason for this is that the formal…
The scattering of spin-polarized electrons in an Aharonov--Bohm vector potential is considered. We solve the Pauli equation in 3+1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment…
The Aharonov-Bohm (AB) effect has been highly influential in fundamental and applied physics. Its topological nature commonly implies that an electron encircling a magnetic flux source in a field-free region must close the loop in order to…
The basic AB problem is to determine how an unshielded tube of magnetic flux $\Phi$ affects arbitrarily long-wavelength charged particles impinging on it. For spin-1 at almost all $\Phi$ the particles do not penetrate the tube, so the…
We analyze spin-0 relativistic scattering of charged particles propagating in the exterior, $\Lambda \subset \mathbb{R}^3$, of a compact obstacle $K \subset \mathbb{R}^3$. The connected components of the obstacle are handlebodies. The…