Related papers: Calculation of the Aharonov-Bohm wave function
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…
Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive…
We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from…
The aim of this paper is to give an explicit formula for the nonsymmetric Heckman-Opdam's hypergeometric function of type $A_2$. This is obtained by differentiating the corresponding symmetric hypergeometric function.
The non-stationary Aharonov-Bohm effect (scattering of electron in the field of a narrow solenoid with alternating current) is considered. Using the eikonal approximation, the wave function of electron, the differential and total scattering…
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…
The scattering amplitude of a charged particle from a long hard cylinderical solenoid is derived by solving the time independent Schr\"{o}dinger equation on a double connected plane. It is a summation over the angular momentum quantum…
We consider the problem of approximating a function using Herglotz wave functions, which are a superposition of plane waves. When the discrepancy is measured in a ball, we show that the problem can essentially be solved by considering the…
In this note we explicitly compute the resonances on hyperbolic cones. These are hyperbolic manifolds with a conic singularity equipped with a warped product metric. The calculation is based on separation of variables and Kummer's…
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…
We consider a Volovik's analog model for description of a topological defects in a superfluid and we investigate the scattering of quasiparticles in this background. The analog of the gravitational Aharonov-Bohm in this system is found. An…
We investigate Aharonov-Bohm oscillations of the current through a strongly correlated quantum dot embedded in an arbitrary scattering geometry. Resonant-tunneling processes lead to a flux-dependent renormalization of the dot level. As a…
Quantum-mechanical scattering of nonrelativistic charged particles by a magnetic vortex of nonzero transverse size is considered. We show that the flux of the vortex serves as a gate for the strictly forward propagation of particles with…
The Aharonov-Bohm effect on the noncommutative plane is considered. Developing the path integral formulation of quantum mechanics, we find the propagation amplitude for a particle in a noncommutative space. We show that the corresponding…
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…
In ref [1], a criterion has been derived for the objective wave function reduction through the Shr\"odinger-Newton equation. In this paper, we shall derive that criterion by using the concept of Bohmian trajectories. This study has two…
This paper has been heavily revised, the final results now being contained in hep-ph/9311202 and hep-ph/9311203.
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…
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…
We add a confining potential to the Aharonov-Bohm model resulting in no contact of the particle with the solenoid (border); this is characterized by a unique self-adjoint extension of the initial Hamiltonian operator. It is shown that the…