Related papers: Dynamics of the Aharonov-Bohm effect
In the present article we show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing…
Classical electrodynamics foresees that the effective interaction force between a moving charge and a magnetic dipole is modified by the time-varying total momentum of the interaction fields. We derive the equations of motion of the…
The Aharonov-Bohm (AB) effect highlights the fundamental role of electromagnetic potentials in quantum mechanics, manifesting as a phase shift for a charged particle in field-free regions. While well-established for static magnetic fluxes,…
The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schr\"odinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is…
We present an angular--momentum--resolved energetic formulation of the Aharonov--Bohm (AB) response for a confined Dirac electron based on two gauge--invariant interaction functionals: a magnetization--field functional and a…
The time-dependent Aharonov-Bohm (AB) effect considers the situation in which the magnetic flux inside the solenoid changes time-dependently. Different from the standard AB-effect, the problem is unexpectedly subtle and not easy to solve…
In the present article we analyze the problem of a relativistic Dirac electron in the presence of a combination of a Coulomb field, a $1/r$ scalar potential as well as a Dirac magnetic monopole and an Aharonov-Bohm potential. Using the…
The Aharonov-Bohm effect is the prime example of a zero-field-strength configuration where a non-trivial vector potential acquires physical significance, a typical quantum mechanical effect. We consider an extension of the traditional A-B…
We study a multi-determinant approach to the time evolution of the nuclear wave functions (TDMD). We employ the Dirac variational principle and use as anzatz for the nuclear wave-function a linear combination of Slater determinants and…
Whether the time-dependent Aharonov-Bohm (AB) effect even exists or not has been the subject of long-standing debate. There are two factors complicating the problem. First, in the closed spacetime line integral of the vector potential that…
The paper analyzes time propagation of Dirac observables - using Heisenberg representation - in the light of various pseudodifferential operator algebras (cf. [Co3], [Co15], [Co16]). Our theory gives (i) a mechanical angular momentum (the…
The Fermi acceleration mechanism is a significant source of cosmic rays. When the width of a potential well changes over time, the velocity of particles within the well also changes. For quantum systems, such dynamics should be described by…
Following the Dirac-Frenkel time-dependent variational principle, dynamics of a one-dimensional Holstein polaron is probed by employing the Davydov D2 Ansatz with two sets of variational parameters, one for each constituting particle in the…
In this paper we study the dispersive properties of a two dimensional massless Dirac equation perturbed by an Aharonov--Bohm magnetic field. Our main results will be a family of pointwise decay estimates and a full range family Strichartz…
This article investigates some solutions of the time-dependent free Dirac equation. Visualizations of these solutions immediately reveal strange phenomena that are caused by the interference of positive- and negative-energy waves. The…
It is generally admitted that in quantum mechanics, the electromagnetic potentials have physical interpretations otherwise absent in classical physics as illustrated by the Aharonov-Bohm effect. In 1984, Berry interpreted this effect as a…
In this article, we study topological and noninertial effects on the motion of the two-dimensional Dirac oscillator in the presence of a uniform magnetic field and the Aharonov-Bohm potential. We obtain the Dirac equation that describes the…
The solution of Dirac's equation for the hydrogen atom according to relativistic wave mechanics yields for each state a vectorial amplitude function with four components, two large and two small. Each such component has its characteristic…
We show that for a particular choice of gauge the vector potential of any non-radiating source is spatially localized along with its electric and magnetic fields. Important on its own, this special property of non-radiating sources…
The behaviour of the Dirac field in FRW space-time is investigated. The relevant equations are solved to determine the particle and energy distribution. The angular and radial parts are solved in terms of Jacobi polynomials. The time…