scholarly journals Generalized boundary conditions for the Aharonov–Bohm effect combined with a homogeneous magnetic field

2002 ◽  
Vol 43 (5) ◽  
pp. 2151 ◽  
Author(s):  
P. Exner ◽  
P. Št’ovı́ček ◽  
P. Vytřas
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Homogeneous Magnetic Field ◽  
Bohm Effect ◽  
Generalized Boundary Conditions ◽  
Aharonov Bohm

scholarly journals A general method for deriving vector potentials produced by knotted solenoids

2014 ◽  
Vol 29 (35) ◽  
pp. 1450189
Author(s):  
V. V. Sreedhar
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Vector Potentials ◽  
Bohm Effect ◽  
Figure Eight Knot ◽  
Aharonov Bohm ◽  
The Magnetic Field ◽  
General Method

A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented. It consists of using simple physics ideas from magnetostatics to evaluate the magnetic field in a surrogate problem. The latter is obtained by modeling the knot with wire segments carrying steady currents on a cubical lattice. The expressions for a 31 (trefoil) and a 41 (figure-eight) knot are explicitly worked out. The results are of some importance in the study of the Aharonov–Bohm effect generalized to a situation in which charged particles moving through force-free regions are scattered by fluxes confined to the interior of knotted impenetrable tubes.

scholarly journals The non-ideal theory of the Aharonov–Bohm effect

Synthese ◽  
2020 ◽  
Author(s):  
John Dougherty
Keyword(s):  
Boundary Conditions ◽  
Electromagnetic Interaction ◽  
Theoretical Description ◽  
Ideal Theory ◽  
Topological Interpretation ◽  
Singular Limits ◽  
Bohm Effect ◽  
The Common ◽  
Aharonov Bohm

Abstract Elay Shech and John Earman have recently argued that the common topological interpretation of the Aharonov–Bohm (AB) effect is unsatisfactory because it fails to justify idealizations that it presupposes. In particular, they argue that an adequate account of the AB effect must address the role of boundary conditions in certain ideal cases of the effect. In this paper I defend the topological interpretation against their criticisms. I consider three types of idealization that might arise in treatments of the effect. First, Shech takes the AB effect to involve an idealization in the form of a singular limit, analogous to the thermodynamic limit in statistical mechanics. But, I argue, the AB effect itself features no singular limits, so it doesn’t involve idealizations in this sense. Second, I argue that Shech and Earman’s emphasis on the role of boundary conditions in the AB effect is misplaced. The idealizations that are useful in connecting the theoretical description of the AB effect to experiment do interact with facts about boundary conditions, but none of these idealizations are presupposed by the topological interpretation of the effect. Indeed, the boundary conditions for which Shech and demands justification are incompatible with some instances of the AB effect, so the topological interpretation ought not justify them. Finally, I address the role of the non-relativistic approximation usually presumed in discussions of the AB effect. This approximation is essential if—as the topological interpretation supposes—the AB effect constrains and justifies a relativistic theory of the electromagnetic interaction. In this case the ends justify the means. So the topological view presupposes no unjustified idealizations.

Aharonov-Bohm effect under high magnetic field in a Corbino disk anti-dot channel

1992 ◽  
Vol 263 (1-3) ◽  
pp. 392-395 ◽  
Author(s):  
Kotaro Tsubaki ◽  
Takashi Honda ◽  
Yasuhiro Tokura
Keyword(s):  
Magnetic Field ◽  
High Magnetic Field ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Corbino Disk

scholarly journals Generalized KG-oscillator with a uniform magnetic field under the influence of Coulomb-type potentials in cosmic string space-time and Aharonov-Bohm effect

2021 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Magnetic Field ◽  
Cosmic String ◽  
Uniform Magnetic Field ◽  
Bound States ◽  
Space Time ◽  
Vector Potentials ◽  
Klein Gordon ◽  
Relativistic Analogue ◽  
Bohm Effect ◽  
Aharonov Bohm

We solve a generalized Klein-Gordon oscillator (KGO) in the presence of a uniform magnetic field including quantum flux under the effects of a scalar and vector potentials of Coulomb-types in the static cosmic string space-time. We obtain the energy and corresponding eigenfunctions, and analyze a relativistic analogue of the Aharonov-Bohm effect for bound states.

Two-state magnetic field Aharonov–Bohm effect and the wave–particle duality in a Mach–Zehnder interferometer

2017 ◽  
Vol 15 (05) ◽  
pp. 1750032 ◽  
Author(s):  
M. Bendahane ◽  
M. El Atiki ◽  
A. Kassou-Ou-Ali
Keyword(s):  
Magnetic Field ◽  
Zehnder Interferometer ◽  
Experimental Scheme ◽  
Wave Particle Duality ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Mach Zehnder Interferometer

In this work, we study the wave particle duality and the Aharonov–Bohm effect in a Mach–Zehnder interferometer in a magnetic field which is in a superposition of two opposite directions. In addition, a “classical” experimental scheme is proposed which mimics such an interferometer.

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