Journal of Physics A Mathematical and Theoretical

Duality in the Aharonov–Casher and Aharonov–Bohm effects

Daniel Rohrlich

Published Aug 12, 2010• 4 citations

Abstract

A neutral particle with a magnetic moment interacts with a charged particle. Such an interaction is invariant under the interchange of the particles. This interchangeability or duality of the particles elucidates subtleties of the Aharonov?Bohm and Aharonov?Casher effects, including whether and how these two effects are themselves dual.

DOI: 10.1088/1751-8113/43/35/354028

Related papers

The Aharonov-Casher Effect for Particles of Arbitrary Spin

Ya. I. Azimov, R.M. Ryndin

The Aharonov-Casher (AC) effect for quantum motion of a neutral magnetized particle in the electric field is believed to be a topological effect closely related to the known Aharonov-Bohm (AB) effect. We study how it depends on the spin of the particle involved. Duality of the AB and AC effects is demonstrated to exist only for two extreme spin (and magnetic moment) projections. Classical consideration confirms the conclusion. Motion of a classical magnetized particle with generally oriented magnetic moment in the AC field appears to be subjected to both forces and torques. Only for two special orientations of the magnetic moment (same as in the quantum case) the motion is effectively free and similar to the AB motion of a charged particle. Thus, the AC effect is not really topological. Presence of higher multipoles totally destroys the possible AB-AC duality.

arXiv:hep-ph/9710433Physics of Atomic NucleiOct 22, 19971 citation

(Semi)classical motion in fields of Aharonov-Bohm and Aharonov-Casher

Ya. I. Azimov, R.M. Ryndin

Particle motion in the fields of Aharonov-Bohm and Aharonov-Casher is considered in framework of the classical theory to reveal conditions admitting duality of the two configurations. Important role of orientation of the magnetic dipole moment is demonstrated. Duality becomes totally destroyed by addition of electric dipole and/or higher multipole moments. Correspondence between quantum and classical considerations is also discussed.

arXiv:hep-ph/9707468Jul 25, 19970 citations

THE AHARONOV-CASHER EFFECT

In 1984, 25 years after the prediction of the →Aharonov-Bohm (AB) effect, Aharonov and Casher [1] predicted a “dual ” effect. In both effects, a particle is excluded from a tubular region of space, but otherwise no force acts on it. Yet it acquires a measurable quantum phase that depends on what is inside the tube of space from which it is excluded. In the AB effect, the particle is charged and the tube contains a magnetic flux. In the Aharonov-Casher (AC) effect, the particle is neutral, but has a magnetic moment, and the tube contains a line of charge. Experiments in neutron [2], vortex [3], atom [4], and electron [5] interferometry bear out the prediction of Aharonov and Casher. Here we briefly explain the logic of the AC effect and how it is dual to the AB effect. We begin with a two-dimensional version of the AB effect. Figure 1 shows an electron moving in a plane, and also a “fluxon”, i.e. a small region of magnetic flux (pointing out of the plane) from which the electron is excluded. In Fig. 1 the fluxon is in a quantum superposition of two positions, and the electron diffracts around one of the positions but not the other. Initially, the fluxon and electron are in a

Nov 26, 20120 citations

Topological Quantum Effects for Neutral Particles

Yakir Aharonov, A. Casher

We derive the effective Lagrangian which describes the interaction between a charged particle and a magnetic moment in the nonrelativistic limit. It is shown that neutral particles with a magnetic moment will exhibit the Aharonov-Bohm effect in certain circumstances. We suggest several types of experiments.

Physical Review LettersJul 23, 19841,261 citations

Aharonov-Casher effect and geometrical phases

R Mignani

The phaseshift experienced by a neutral particle with a magnetic moment as it encircles an infinite line of charge (Aharonov-Casher effect) (1984) is derived as a special case of geometrical phases, i.e. the standard Berry phase and the gauge-invariant Yang phase.

Journal of Physics A Mathematical and GeneralApr 21, 199125 citations

What did we learn from the Aharonov-Bohm effect? Is spin 1/2 different?

Michael A. Peshkin

I review what has been learned about fundamental issues in quantum mechanics from the Aharonov-Bohm effect. Following that, I consider the Aharonov-Casher effect and the Scalar Aharonov-Bohm effect, in both of which a spin-1/2 particle interacts with a local electromagnetic field through its magnetic moment, and conclude that those effects can be described as observable effects of local torques.

Jun 1, 19940 citations