Topology, Locality, and Aharonov-Bohm Effect with Neutrons

Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the electron's charge. We show that the new phenomenon, called Scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue that the SAB effect is not a topological effect by any useful definition. We find that SAB actually measures an apparently novel spin autocorrelation whose operator equations of motion contain the local torque in the magnetic field. We note that the same remarks apply to the Aharonov-Casher effect.Comment: 9 page

Darwin-Lagrangian Analysis for the Interaction of a Point Charge and a Magnet: Considerations Related to the Controversy Regarding the Aharonov-Bohm and Aharonov-Casher Phase Shifts

The classical electromagnetic interaction of a point charge and a magnet is discussed by first calculating the interaction of point charge with a simple model magnetic moment and then suggesting a multiparticle limit. The Darwin Lagrangian is used to analyze the electromagnetic behavior of the model magnetic moment (composed of two oppositely charged particles of different mass in an initially circular orbit) interacting with a passing point charge. The changing mangetic moment is found to put a force back on a passing charge; this force is of order 1/c^2 and depends upon the magnitude of the magnetic moment. It is suggested that in the limit of a multiparticle magnetic toroid, the electric fields of the passing charge are screened out of the body of the magnet while the magnetic fields penetrate into the magnet. This is consistent with our understanding of the penetration of electromagnetic velocity fields into ohmic conductors. Conservation laws are discussed. The work corresponds to a classical electromagnetic analysis of the interaction which is basic to understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase shifts and represents a refutation of the suggestions of Aharonov, Pearle, and Vaidman.Comment: 33 page

Levinson theorem for Aharonov-Bohm scattering in two dimensions

We apply the recently generalized Levinson theorem for potentials with inverse square singularities [Sheka et al, Phys.Rev.A, v.68, 012707 (2003)] to Aharonov-Bohm systems in two-dimensions. By this theorem, the number of bound states in a given m-th partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.Comment: 5 pages (REVTeX

Local/Non-Local Complementarity in Topological Effects

In certain topological effects the accumulation of a quantum phase shift is accompanied by a local observable effect. We show that such effects manifest a complementarity between non-local and local attributes of the topology, which is reminiscent but yet different from the usual wave-particle complementarity. This complementarity is not a consequence of non-commutativity, rather it is due to the non-canonical nature of the observables. We suggest that a local/non-local complementarity is a general feature of topological effects that are ``dual'' to the AB effect.Comment: 4 page

Remarks on the Configuration Space Approach to Spin-Statistics

The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connection with other configuration space approaches to spin-statistics is discussed, as well as the relevance of the obtained results in view of a possible alternative proof of the spin-statistics theorem.Comment: 18 page

Aharonov-Bohm interference in the presence of metallic mesoscopic cylinders

This work studies the interference of electrons in the presence of a line of magnetic flux surrounded by a normal-conducting mesoscopic cylinder at low temperature. It is found that, while there is a supplementary phase contribution from each electron of the mesoscopic cylinder, the sum of these individual supplementary phases is equal to zero, so that the presence of a normal-conducting mesoscopic ring at low temperature does not change the Aharonov-Bohm interference pattern of the incident electron. It is shown that it is not possible to ascertain by experimental observation that the shielding electrons have responded to the field of an incident electron, and at the same time to preserve the interference pattern of the incident electron. It is also shown that the measuring of the transient magnetic field in the region between the two paths of an electron interference experiment with an accuracy at least equal to the magnetic field of the incident electron generates a phase uncertainty which destroys the interference pattern.Comment: 15 pages, 5 Postscript figure

The Aharonov-Bohm effect: the role of tunneling and associated forces

Through tunneling, or barrier penetration, small wavefunction tails can enter a finitely shielded cylinder with a magnetic field inside. When the shielding increases to infinity the Lorentz force goes to zero together with these tails. However, it is shown, by considering the radial derivative of the wavefunction on the cylinder surface, that a flux dependent force remains. This force explains in a natural way the Aharonov-Bohm effect in the idealized case of infinite shielding.Comment: 13 pages, 3 figures; minor changes, references added, typo corrected in eq. (16). Accepted for publication in Journal of Physics

Directional speakers as a tool for animal vocal communication studies

Audio playbacks are a common experimental tool in vocal communication research. However, low directionality of sound makes it hard to control the audience exposed to the stimuli. Parametric speakers offer a solution for transmitting directional audible signals by using ultrasonic carrier waves. The targeted transmission of vocal signals offers exciting opportunities for testing the diffusion of information in animal groups and mechanisms for resolving informational ambiguities. We have field tested the quality and directionality of a commercial parametric speaker, Soundlazer SL-01. Additionally, we assessed its usability for performing playback experiments by comparing behavioural responses of free-ranging meerkats (Suricata suricatta) with calls transmitted from conventional and parametric speakers. Our results show that the tested parametric speaker is highly directional. However, the acoustic structure of meerkat calls was strongly affected and low frequencies were not reliably reproduced by the parametric speaker. The playback trials elicited weakened behavioural responses probably due to the partial distortion of the signal but also indicating the potential importance of social facilitation for initiating mobbing events in meerkats. We conclude that parametric speakers can be useful tools for directed transmission of animals calls but after a careful assessment of signal fidelity

Unbroken supersymmetry in the Aharonov-Casher effect

We consider the problem of the bound states of a spin 1/2 chargless particle in a given Aharonov-Casher configuration. To this end we recast the description of the system in a supersymmetric form. Then the basic physical requirements for unbroken supersymmetry are established. We comment on the possibility of neutron confinement in this system

Magnetic Force Exerted by the Aharonov-Bohm Line

The problem of the scattering of a charge by the Aharonov-Bohm (AB) flux line is reconsidered in terms of finite width beams. It is shown that despite the left-right symmetry in the AB scattering cross-section, the charge is scattered asymmetrically. The asymmetry (i.e. magnetic force) originates from almost forward scattering within the angular size of the incident wave. In the paraxial approximation, the real space solution to the scattering problem of a beam is found as well as the scattering S-matrix. The Boltzmann kinetics and the Landau quantization in a random AB array are considered.Comment: 5 pages, RevTeX. Discussions of paraxial approximation to the Aharonov-Bohm solution (Cornu spiral) and S-matrix, are extended. References are adde