Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1508.07806 · Annalen der Physik

Semiclassical Asymptotics of the Aharonov‐Bohm Interference Process

S. Fischer, Clemens Gneiting, Andreas Buchleitner

Published Aug 14, 2017• 0 citations
arXivHTMLPDF

Abstract

Abstract We systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart. A picture of Aharonov‐Bohm interference of two half‐waves acquiring Dirac's magnetic phase when passing on either side of the solenoid naturally emerges from the quantum propagator. The resulting interference pattern is fully determined by the ratio of the angular part of Hamilton's principal function to Planck's constant, and the wave interference smoothes out discontinuities in the semiclassical propagator which is recovered in the limit when the above ratio diverges. We discuss the relation of our results to the whirling‐wave representation of the exact propagator, and to previous approaches on the system's asymptotics.

DOI
10.1002/andp.201700120

Related papers

Semiclassical asymptotics of the Aharonov-Bohm interference process

S. Fischer, Clemens Gneiting, Andreas Buchleitner

Abstract We systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart. A picture of Aharonov‐Bohm interference of two half‐waves acquiring Dirac's magnetic phase when passing on either side of the solenoid naturally emerges from the quantum propagator. The resulting interference pattern is fully determined by the ratio of the angular part of Hamilton's principal function to Planck's constant, and the wave interference smoothes out discontinuities in the semiclassical propagator which is recovered in the limit when the above ratio diverges. We discuss the relation of our results to the whirling‐wave representation of the exact propagator, and to previous approaches on the system's asymptotics.

•Jan 1, 2017•0 citations

Scattering of a charged particle from a hard cylindrical solenoid: Aharonov-Bohm Effect

Oktay Yilmaz

The scattering amplitude of a charged particle from a long hard cylinderical solenoid is derived by solving the time independent Schrödinger equation on a double connected plane. It is a summation over the angular momentum quantum number (partial wave summation). It is shown that only negative mechanical angular momenta contribute to the amplitude when the radius of the solenoid goes to zero limit without varying the magnetic induction flux (Flux line). Original Aharonov-Bohm result is obtained with this limit.

arXiv:1311.6924•Chinese Journal of Physics•Nov 27, 2013•2 citations

Aharonov-Bohm Effect for Electron Phase Representing a Quantum Mechanical Average Value

Vladan Panković, D. Kapor

In the usual Aharonov-Bohm effect, representing an especial case of the Berry phase phenomenon, classical magnetic field within long and thin solenoid (or classical vector potential of the electromagnetic field without this solenoid) causes phase difference and interference shape translation of the quantum propagating (external) electron. In this work we consider a variation of the usual Aharonov-Bohm effect with two solenoids sufficiently close one to the other so that (external) electron cannot propagate between two solenoids but only around both solenoids. Here magnetic field (or classical vector potential of the electromagnetic field) acting at quantum propagating (external) electron represents the quantum mechanical average value or statistical mixture. It is obtained by wave function of single (internal, quantum propagating within some solenoid wire) electron (or homogeneous ensemble of such (internal) electrons) representing a quantum superposition with two practically non-interfering terms. All this implies that phase difference and interference shape translation of the quantum propagating (external) electron represent the quantum mechanical average value or statistical mixture. In this way we obtain a very interesting generalization of the usual Aharonov-Bohm effect and Berry phase concept. As it is well-known in the usual experimental arrangement corresponding to the AharonovBohm effect [1]-[4] (representing an especial case of the Berry phase phenomenon [4], [5]) behind a diaphragm with two slits there is a long and very thin solenoid (placed perpendicularly, i.e. in the z-axis direction, to the x-0-y plane of the propagation of the (external, without solenoid

arXiv:1007.2538•Jul 15, 2010•0 citations

Electromagnetic momentum in the Aharonov–Bohm quantum interference experiment from a physical perspective

Ashok K. Singal

In the Aharonov–Bohm setup, a double-slit experiment, when a long but thin solenoid of current is introduced between the two coherent beams of electrons behind the slits, an extra phase difference between the interfering beams appears, as shown by a shift in the interference pattern. This mysterious effect purportedly arises owing to an electromagnetic momentum, attributed to the presence of a vector potential at the location of either beam, due to the solenoid of current even when the magnetic field is zero outside the solenoid. It has remained a puzzle, how mere potential, thought to be just a mathematical tool for calculating electromagnetic field, can give rise to electromagnetic momentum in a system. Experimentally, the effect has been amply verified, with hardly any doubts that the observed effect is real. A satisfactory physical explanation of the existence of momentum, at least under the aegis of classical electromagnetism, is still missing since inception of the idea more than half a century back. We show here the presence of electromagnetic momentum in the product of the drift velocities of the current-carrying charges within the solenoid and the mass equivalent of their potential energies in the electric field of the external charges.

arXiv:2301.06502•Canadian Journal of Physics•Jan 1, 2026•0 citations

Finite and half-infinite solenoids and the Aharonov-Bohm effect

Joel Franklin, Gopal Goel

In quantum mechanics, the magnetic field has a physical effect beyond its local presence. For axially symmetric vector potentials, A=A(s,z)ϕ̂, it is the magnetic flux that plays a central role in both interference experiments (as in the Aharonov-Bohm effect) and in bound state spectra for a particle constrained to move in a circle. The flux dependence is evident in various configurations, and we have chosen two applications to highlight the non-local nature of the quantum mechanical magnetic field dependence: A finite solenoid and a Dirac string with a non-zero radius. The finite solenoid is interesting because it represents the actual experimental apparatus for measuring the Aharonov-Bohm effect. The Dirac string provides an electric charge quantization mechanism that depends on where the quantization argument is applied, yielding different fundamental charge units for different locations.

American Journal of Physics•Oct 18, 2019•2 citations

Solvable models in the scattering theory for the Aharonov-Bohm effect (Tosio Kato Centennial Conference)

Takuya Mine

We briefly review the scattering theory for the Schrödinger operator related to the Aharonov-Bohm effect, by exhibiting some explicitly solvable models; an infinitesimally thin solenoid in mathbb{R}^{2}, two infinitesimally thin solenoids with the quantized magnetic fluxes in mathbb{R}^{2}, and an infinitesimally thin ring solenoid with the quantized magnetic flux in mathbb{R}^{3}. We give explicit formulas for the incoming wave solution and the scattering amplitude for these models in terms of some special functions, with the graphs obtained by a numerical method. We also review known high-energy asymptotic formulas related to these examples.

数理解析研究所講究録•Jul 1, 2018•0 citations
Abstract We systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart. A picture of Aharonov‐Bohm interference of two half‐waves acquiring Dirac's magnetic phase when passing on either side of the solenoid naturally emerges from the quantum propagator. The resulting interference pattern is fully determined by the ratio of the angular part of Hamilton's principal function to Planck's constant, and the wave interference smoothes out discontinuities in the semiclassical propagator which is recovered in the limit when the above ratio diverges. We discuss the relation of our results to the whirling‐wave representation of the exact propagator, and to previous approaches on the system's asymptotics.
Abstract We systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart. A picture of Aharonov‐Bohm interference of two half‐waves acquiring Dirac's magnetic phase when passing on either side of the solenoid naturally emerges from the quantum propagator. The resulting interference pattern is fully determined by the ratio of the angular part of Hamilton's principal function to Planck's constant, and the wave interference smoothes out discontinuities in the semiclassical propagator which is recovered in the limit when the above ratio diverges. We discuss the relation of our results to the whirling‐wave representation of the exact propagator, and to previous approaches on the system's asymptotics.
The scattering amplitude of a charged particle from a long hard cylinderical solenoid is derived by solving the time independent Schrödinger equation on a double connected plane. It is a summation over the angular momentum quantum number (partial wave summation). It is shown that only negative mechanical angular momenta contribute to the amplitude when the radius of the solenoid goes to zero limit without varying the magnetic induction flux (Flux line). Original Aharonov-Bohm result is obtained with this limit.
In the usual Aharonov-Bohm effect, representing an especial case of the Berry phase phenomenon, classical magnetic field within long and thin solenoid (or classical vector potential of the electromagnetic field without this solenoid) causes phase difference and interference shape translation of the quantum propagating (external) electron. In this work we consider a variation of the usual Aharonov-Bohm effect with two solenoids sufficiently close one to the other so that (external) electron cannot propagate between two solenoids but only around both solenoids. Here magnetic field (or classical vector potential of the electromagnetic field) acting at quantum propagating (external) electron represents the quantum mechanical average value or statistical mixture. It is obtained by wave function of single (internal, quantum propagating within some solenoid wire) electron (or homogeneous ensemble of such (internal) electrons) representing a quantum superposition with two practically non-interfering terms. All this implies that phase difference and interference shape translation of the quantum propagating (external) electron represent the quantum mechanical average value or statistical mixture. In this way we obtain a very interesting generalization of the usual Aharonov-Bohm effect and Berry phase concept. As it is well-known in the usual experimental arrangement corresponding to the AharonovBohm effect [1]-[4] (representing an especial case of the Berry phase phenomenon [4], [5]) behind a diaphragm with two slits there is a long and very thin solenoid (placed perpendicularly, i.e. in the z-axis direction, to the x-0-y plane of the propagation of the (external, without solenoid
In the Aharonov–Bohm setup, a double-slit experiment, when a long but thin solenoid of current is introduced between the two coherent beams of electrons behind the slits, an extra phase difference between the interfering beams appears, as shown by a shift in the interference pattern. This mysterious effect purportedly arises owing to an electromagnetic momentum, attributed to the presence of a vector potential at the location of either beam, due to the solenoid of current even when the magnetic field is zero outside the solenoid. It has remained a puzzle, how mere potential, thought to be just a mathematical tool for calculating electromagnetic field, can give rise to electromagnetic momentum in a system. Experimentally, the effect has been amply verified, with hardly any doubts that the observed effect is real. A satisfactory physical explanation of the existence of momentum, at least under the aegis of classical electromagnetism, is still missing since inception of the idea more than half a century back. We show here the presence of electromagnetic momentum in the product of the drift velocities of the current-carrying charges within the solenoid and the mass equivalent of their potential energies in the electric field of the external charges.
In quantum mechanics, the magnetic field has a physical effect beyond its local presence. For axially symmetric vector potentials, A=A(s,z)ϕ̂, it is the magnetic flux that plays a central role in both interference experiments (as in the Aharonov-Bohm effect) and in bound state spectra for a particle constrained to move in a circle. The flux dependence is evident in various configurations, and we have chosen two applications to highlight the non-local nature of the quantum mechanical magnetic field dependence: A finite solenoid and a Dirac string with a non-zero radius. The finite solenoid is interesting because it represents the actual experimental apparatus for measuring the Aharonov-Bohm effect. The Dirac string provides an electric charge quantization mechanism that depends on where the quantization argument is applied, yielding different fundamental charge units for different locations.
We briefly review the scattering theory for the Schrödinger operator related to the Aharonov-Bohm effect, by exhibiting some explicitly solvable models; an infinitesimally thin solenoid in mathbb{R}^{2}, two infinitesimally thin solenoids with the quantized magnetic fluxes in mathbb{R}^{2}, and an infinitesimally thin ring solenoid with the quantized magnetic flux in mathbb{R}^{3}. We give explicit formulas for the incoming wave solution and the scattering amplitude for these models in terms of some special functions, with the graphs obtained by a numerical method. We also review known high-energy asymptotic formulas related to these examples.