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This paper addresses the scattering of a beam of charged particles by an infinitely long magnetic string in the context of the hydrodynamical approach to quantum mechanics. The scattering is qualitatively analyzed by two approaches. In the…
The Aharonov-Bohm electrodynamics is a generalization of Maxwell theory with reduced gauge invariance. It allows to couple the electromagnetic field to a charge which is not locally conserved, and has an additional degree of freedom, the…
The Aharonov-Bohm 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…
By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary $m$-state in two-dimensional Schr\"{o}dinger wave equation with various power interaction potentials in constant magnetic and…
We consider the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov--Bohm solenoid field and a collinear uniform magnetic field). Using von Neumann's theory of the self-adjoint extensions of symmetric operators,…
Quantum-mechanical scattering off a magnetic vortex is considered, and the optical theorem is derived. The vortex core is assumed to be impermeable to scattered particles, and its transverse size is taken into account. We show that the…
Using the theory of self-adjoint extensions, we construct all the possible hamiltonians describing the non relativistic Aharonov-Bohm effect. In general the resulting hamiltonians are not rotationally invariant so that the angular momentum…
Magnetostatics defines a class of boundary value problems in which the topology of the domain plays a subtle role. For example, representability of a divergence-free field as the curl of a vector potential comes about because of homological…
The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from…
We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple one by taking its semi-direct product with its Lie algebra. We find that the standard knot…
We utilize the coset construction to derive the effective field theory of magnon-phonon interactions in (anti)-ferromagnetic and ferrimagnetic insulating materials. The action is used to calculate the equations of motion which generalize…
Electron transport in a two-terminal Aharonov-Bohm ring with a few short-range scatterers is investigated. An analytical expression for the conductance as a function of the electron Fermi energy and magnetic flux is obtained using the…
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…
Thermodynamics of magnetic materials is discussed in practical, lab-oriented terms. In the common experimental configuration in which the external magnetic field comes from a solenoidal coil connected to a power supply, magnetic work is…
By using the complex angular momentum method, we provide a semiclassical analysis of electron scattering by a magnetic vortex of Aharonov-Bohm-type. Regge poles of the $S$-matrix are associated with surface waves orbiting around the vortex…
The use of a (quasi)uniform magnetic field opens new possibilities for a production of twisted particles having orbital angular momenta. Quantum states suitable for a production of charged particles in a uniform magnetic field are…
This scientific essay proposes to discuss the physical aspects of a system consisting of some non-relativistic massive charged particles, that are the sources in motion of an electromagnetic field (e.m.) propagating through the space,…
A type-II superconductor survives in an external magnetic field by admitting an Abrikosov lattice of quantized vortices. This is an imprint of the Aharonov-Bohm effect created by the Abelian U(1) gauge field. The simplest non-Abelian…
It is presented, in the framework of nonrelativistic quantum mechanics, a justification of the usual Aharonov-Bohm hamiltonian (with solenoid of radius greater than zero). This is obtained by way of increasing sequences of finitely long…
The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally {\normalsize{}U(1)}-gauge invariant, admits linear…