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arXiv:cond-mat/9803105

Aharonov-Bohm and Aharonov-Casher Effects: Connections to Dynamics of Topological Singularities

Ping Ao, Niu, Q.

Published Mar 10, 1998• 0 citations
arXivHTMLPDF

Abstract

We analyze the physical processes involved in the Aharonov-Bohm (A-B) and the Aharonov-Casher (A-C) effects, showing that an incomplete A-B effect knowledge can lead a totally wrong conclusion on the A-C effect. Based on this we demonstrate that the Magnus force, the net force, is the only transverse force on a moving vortex, in analogous to the net charge in A-C effect. This conclusion has been arrived both theoretically and experimentally.

DOI
10.48550/arxiv.cond-mat/9803105

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We analyze the physical processes involved in the Aharonov-Bohm (A-B) and the Aharonov-Casher (A-C) effects, showing that an incomplete A-B effect knowledge can lead a totally wrong conclusion on the A-C effect. Based on this we demonstrate that the Magnus force, the net force, is the only transverse force on a moving vortex, in analogous to the net charge in A-C effect. This conclusion has been arrived both theoretically and experimentally.
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
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.
The forces on the vortex, transverse to its velocity, are considered. In addition to the superfluid Magnus force from the condensate (superfluid component), there are transverse forces from thermal quasiparticles and external fields violating the Galilean invariance. The forces between quasiparticles and the vortex originate from interference of quasiparticles with trajectories on the left and on the right from the vortex like similar forces for electrons interacting with the thin magnetic-flux tube (the Aharonov-Bohm effect). These forces are derived for phonons from the equations of superfluid hydrodynamics, and for BCS quasiparticles from the Bogolyubov--de Gennes equations. The effect of external fields breaking Galilean invariance is analyzed for vortices in the two-dimensional Josephson junction array. The symmetry analysis of the classical equations for the array shows that the total transverse force on the vortex vanishes. Therefore the Hall effect which is linear in the transverse force is absent also. This means that the Magnus force from the superfluid component exactly cancels with the transverse force from the external fields. The results of other approaches are also brought together for discussion.
The Aharonov–Bohm effect was discovered as a quantum-mechanical effect for charged particles, but it has its counterpart in classical wave mechanics. The Aharonov–Bohm interference arises at the scattering of a sound wave by a vortex in classical and quantum hydrodynamics. This interference leads to a transverse force between quasiparticles and vortices in superfluids and superconductors. The Aharonov–Bohm effect was also generalized to neutral particles with magnetic or electric dipole momenta. The Aharonov–Bohm effect for charge particles and its modification for magnetic momenta (the Aharonov–Casher effect) have already been experimentally observed, and the efforts to detect the Aharonov–Bohm effect for electrically polarized neutral particles are on the way. A possible system for this detection is a Bose-condensate of excitons in a double quantum well. Observation of the Aharonov–Bohm effect in this system would provide direct evidence of Bose–Einstein condensation.