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

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Missing He–McKellar–Wilkens geometric quantum phase

K. Bakke

Published Mar 1, 2022• 4 citations
Publisher

Abstract

We discuss the appearance of a missing geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with the magnetic field produced by a uniform distribution of the magnetic charges inside an infinitely long non-conductor cylinder with an inner radius r a . This geometric quantum phase is associated with the missing magnetic charge per unit length in a region with a cylindrical shape of radius r a and gives rise to an analogue of the He–McKellar–Wilkens geometric quantum phase. By searching for bound state solutions, we show that an Aharonov–Bohm-type effect arises from the influence of the missing geometric quantum phase on the eigenvalues of energy.

DOI
10.1098/rspa.2021.0434

Related papers

Missing Aharonov-Casher geometric quantum phase

K. Bakke, Claudio Furtado

From the interaction of the permanent magnetic dipole moment of a neutral particle with an electric field inside a long nonconducting cylindrical shell of inner radius ${r}_{a}$ and outer radius ${r}_{b}$, we show that a geometric quantum phase stems from the missing electric charge per unit length. Thus, we discuss the possibility of existing Aharonov-Bohm-type effects with regard to this geometric quantum phase. Further, we discuss the persistent spin currents.

arXiv:2502.18544•Physical Review A•Dec 13, 2024•5 citations

Quantum dynamics of magnetic and electric dipoles and the geometric phase

Claudio Furtado, Carlos Alberto de Lima Ribeiro

We study the quantum dynamics of a neutral particle that posseses a permanent magnetic and electric dipole moments in the presence of an electromagnetic field. The analysis of this dynamics demonstrates the appearance of a quantum phase that combines the Aharonov-Casher effect and the He-Mckellar-Wilkens effect. We demonstrate that this phase is a special case of the geometric quantum phase. A series of field configurations where this phase would be found is presented. A generalized Casella-type effect is found in one of these configurations. A physical scenario for the quantum phase in an interferometric experiment is proposed.

arXiv:quant-ph/0306090•Physical Review A•Jun 9, 2004•46 citations

Geometric quantum phase in the spacetime of topological defects

K. Bakke, Claudio Furtado, Jose Roberto Nascimento

In this contribution, we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.

Journal of Physics Conference Series•Jul 8, 2011•3 citations

Geometric phase for a neutral particle in the presence of a topological defect

K. Bakke, Jose Roberto Nascimento, Claudio Furtado

In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.

arXiv:0803.3428•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Sep 3, 2008•79 citations

Topological phases reviewed: The Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases

Bruce H. J. McKellar, X-G. He, A. G. Klein

There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of "an electric dipole encircles magnetic charges" was realised experimentally, and discuss possible future experimental realisations.

AIP conference proceedings•Jan 1, 2014•4 citations

From a non-Abelian geometric phase to quantum holonomies for a neutral particle with permanent electric dipole moment

K. Bakke

Abstract By dealing with an elastic medium with a disclination, we search for the influence of the disclination topology on a geometric quantum phase yielded by the interaction of a nonuniform magnetic field with the permanent electric dipole moment of a neutral particle. This magnetic field is produced by a nonuniform electric current density. Further, we explore the non-Abelian nature of the geometric quantum phase in search of quantum holonomies for this neutral particle system and discuss a possible application to the geometric quantum computation.

Quantum Information Processing•Jun 20, 2026•0 citations
We discuss the appearance of a missing geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with the magnetic field produced by a uniform distribution of the magnetic charges inside an infinitely long non-conductor cylinder with an inner radius r a . This geometric quantum phase is associated with the missing magnetic charge per unit length in a region with a cylindrical shape of radius r a and gives rise to an analogue of the He–McKellar–Wilkens geometric quantum phase. By searching for bound state solutions, we show that an Aharonov–Bohm-type effect arises from the influence of the missing geometric quantum phase on the eigenvalues of energy.
From the interaction of the permanent magnetic dipole moment of a neutral particle with an electric field inside a long nonconducting cylindrical shell of inner radius ra{r}_{a}ra​ and outer radius rb{r}_{b}rb​, we show that a geometric quantum phase stems from the missing electric charge per unit length. Thus, we discuss the possibility of existing Aharonov-Bohm-type effects with regard to this geometric quantum phase. Further, we discuss the persistent spin currents.
We study the quantum dynamics of a neutral particle that posseses a permanent magnetic and electric dipole moments in the presence of an electromagnetic field. The analysis of this dynamics demonstrates the appearance of a quantum phase that combines the Aharonov-Casher effect and the He-Mckellar-Wilkens effect. We demonstrate that this phase is a special case of the geometric quantum phase. A series of field configurations where this phase would be found is presented. A generalized Casella-type effect is found in one of these configurations. A physical scenario for the quantum phase in an interferometric experiment is proposed.
In this contribution, we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.
In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.
There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of "an electric dipole encircles magnetic charges" was realised experimentally, and discuss possible future experimental realisations.
Abstract By dealing with an elastic medium with a disclination, we search for the influence of the disclination topology on a geometric quantum phase yielded by the interaction of a nonuniform magnetic field with the permanent electric dipole moment of a neutral particle. This magnetic field is produced by a nonuniform electric current density. Further, we explore the non-Abelian nature of the geometric quantum phase in search of quantum holonomies for this neutral particle system and discuss a possible application to the geometric quantum computation.