scholarly journals Can classical electrodynamics predict nonlocal effects?

2021 ◽  
Vol 136 (8) ◽  
Author(s):  
José A. Heras ◽  
Ricardo Heras
Keyword(s):  
Angular Momentum ◽  
Magnetic Flux ◽  
Classical Electrodynamics ◽  
Local Theory ◽  
Nonlocal Interaction ◽  
Nonlocal Effects ◽  
Classical Counterpart ◽  
Simply Connected Region ◽  
Simply Connected ◽  
Aharonov Bohm

AbstractClassical electrodynamics is a local theory describing local interactions between charges and electromagnetic fields and therefore one would not expect that this theory could predict nonlocal effects. But this perception implicitly assumes that the electromagnetic configurations lie in simply connected regions. In this paper, we consider an electromagnetic configuration lying in a non-simply connected region, which consists of a charged particle encircling an infinitely long solenoid enclosing a uniform magnetic flux, and show that the electromagnetic angular momentum of this configuration describes a nonlocal interaction between the encircling charge outside the solenoid and the magnetic flux confined inside the solenoid. We argue that the nonlocality of this interaction is of topological nature by showing that the electromagnetic angular momentum of the configuration is proportional to a winding number. The magnitude of this electromagnetic angular momentum may be interpreted as the classical counterpart of the Aharonov–Bohm phase.

The Aharonov–Bohm effect and its stationary scattering states from the flat circular annulus U(1) holonomy

2014 ◽  
Vol 11 (10) ◽  
pp. 1450084
Author(s):  
Gabriel Y. H. Avossevou ◽  
Bernadin D. Ahounou
Keyword(s):  
Scattering Problem ◽  
Heisenberg Algebra ◽  
Scattering Data ◽  
Gauge Potential ◽  
Circular Annulus ◽  
Topological Quantum ◽  
Vector Gauge ◽  
Simply Connected ◽  
Aharonov Bohm ◽  
Stationary Scattering

In this paper we study the stationary scattering problem of the Aharonov–Bohm (AB) effect. To achieve this goal we construct a Hamiltonian from the most general representations of the Heisenberg algebra. Such representations are defined on a non-simply-connected manifold which we set as the flat circular annulus. By means of the von Neumann's self-adjoint extensions formalism, the scattering data are then provided. No solenoid is considered in this paper. The corresponding Hamiltonian is based on a topological quantum degree of freedom inherent in such representations. This variable stands for the magnetic vector gauge potential at quantum level. Our outcomes confirm the topological nature of this effect.

Stability of Thin Elastic Plates Covering an Arbitrary Simply Connected Region and Subject to any Admissible Boundary Conditions

1953 ◽  
Vol 20 (1) ◽  
pp. 23-29
Author(s):  
G. A. Zizicas
Keyword(s):  
Boundary Conditions ◽  
Direct Method ◽  
Elastic Plates ◽  
Simple Manner ◽  
Particular Solutions ◽  
Isotropic Plates ◽  
Simply Connected Region ◽  
Simply Connected ◽  
A Direct Method ◽  
Thin Elastic Plates

Abstract The Bergman method of solving boundary-value problems by means of particular solutions of the differential equation, which are constructed without reference to the boundary conditions, is applied to the problem of stability of thin elastic plates of an arbitrary simply connected shape and subject to any admissible boundary conditions. A direct method is presented for the construction of particular solutions that is applicable to both anisotropic and isotropic plates. Previous results of M. Z. Krzywoblocki for isotropic plates are obtained in a simple manner.

Plasmonic Aharonov-Bohm effect: Optical spin as the magnetic flux parameter

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
Yuri Gorodetski ◽  
Sergey Nechayev ◽  
Vladimir Kleiner ◽  
Erez Hasman
Keyword(s):  
Magnetic Flux ◽  
Flux Parameter ◽  
Bohm Effect ◽  
Aharonov Bohm

scholarly journals Magnetic field transport in compact binaries

2020 ◽  
Vol 641 ◽  
pp. A133
Author(s):  
N. Scepi ◽  
G. Lesur ◽  
G. Dubus ◽  
J. Jacquemin-Ide
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Magnetic Flux ◽  
Large Scale ◽  
Compact Object ◽  
Light Curves ◽  
Momentum Transport ◽  
Local Magnetization ◽  
Angular Momentum Transport ◽  
The Impact

Context. Dwarf novæ (DNe) and low mass X-ray binaries (LMXBs) show eruptions that are thought to be due to a thermal-viscous instability in their accretion disk. These eruptions provide constraints on angular momentum transport mechanisms. Aims. We explore the idea that angular momentum transport could be controlled by the dynamical evolution of the large-scale magnetic field. We study the impact of different prescriptions for the magnetic field evolution on the dynamics of the disk. This is a first step in confronting the theory of magnetic field transport with observations. Methods. We developed a version of the disk instability model that evolves the density, the temperature, and the large-scale vertical magnetic flux simultaneously. We took into account the accretion driven by turbulence or by a magnetized outflow with prescriptions taken, respectively, from shearing box simulations or self-similar solutions of magnetized outflows. To evolve the magnetic flux, we used a toy model with physically motivated prescriptions that depend mainly on the local magnetization β, where β is the ratio of thermal pressure to magnetic pressure. Results. We find that allowing magnetic flux to be advected inwards provides the best agreement with DNe light curves. This leads to a hybrid configuration with an inner magnetized disk, driven by angular momentum losses to an MHD outflow, sharply transiting to an outer weakly-magnetized turbulent disk where the eruptions are triggered. The dynamical impact is equivalent to truncating a viscous disk so that it does not extend down to the compact object, with the truncation radius dependent on the magnetic flux and evolving as Ṁ−2/3. Conclusions. Models of DNe and LMXB light curves typically require the outer, viscous disk to be truncated in order to match the observations. There is no generic explanation for this truncation. We propose that it is a natural outcome of the presence of large-scale magnetic fields in both DNe and LMXBs, with the magnetic flux accumulating towards the center to produce a magnetized disk with a fast accretion timescale.

HIGH FREQUENCY AHARONOV–BOHM OSCILLATIONS IN CARBON NANOTUBES

2003 ◽  
Vol 17 (04) ◽  
pp. 159-165
Author(s):  
LINFENG YANG ◽  
JIE JIANG ◽  
JINMING DONG
Keyword(s):  
Carbon Nanotubes ◽  
Magnetic Flux ◽  
High Frequency ◽  
Quantum Interference ◽  
Weak Localization ◽  
Experimental Results ◽  
Single Wall Carbon Nanotubes ◽  
Multiple Cycle ◽  
Breaking Length ◽  
Aharonov Bohm

We give a multiple-cycle quantum interference model and obtain magnetoresistance (MR) expression in the framework of the weak localization. The MR expression based upon finite phase-breaking length Lφ can explain well several experimental results about distinct negative magnetoresistance of carbon nanotubes. The higher-order oscillation peaks with magnetic flux exist in the MR can also be explained by our model. And a new method to measure the phase-breaking length Lφ of the single-wall carbon nanotubes has been proposed.

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