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arXiv:1002.1250 · Journal of Physics A Mathematical and Theoretical

The Aharonov–Bohm effect in conical space

Yurii A Sitenko, Nadiia D Vlasii

Published Aug 12, 2010• 5 citations
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Abstract

Conical space emerges inevitably as an outer space of any topological defect of the vortex type. Quantum-mechanical scattering of a nonrelativistic particle by a vortex centred in conical space is considered, and effects of the transverse size of the vortex are taken into account. Paradoxical peculiarities of scattering in the short-wavelength limit are discussed.

DOI
10.1088/1751-8113/43/35/354014

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Journal of Physics A Mathematical and Theoretical•Aug 12, 2010•9 citations
Conical space emerges inevitably as an outer space of any topological defect of the vortex type. Quantum-mechanical scattering of a nonrelativistic particle by a vortex centred in conical space is considered, and effects of the transverse size of the vortex are taken into account. Paradoxical peculiarities of scattering in the short-wavelength limit are discussed.
Quantum-mechanical scattering off a magnetic vortex is considered, and the optical theorem is derived. The vortex core is assumed to be impermeable to scattered particles, and its transverse size is taken into account. We show that the scattering Aharonov–Bohm effect is independent of the choice of boundary conditions from the variety of the Robin ones. The behaviour of the scattering amplitude in the forward direction is analysed, and the persistence of the Fraunhofer diffraction in the short-wavelength limit is shown to be crucial for maintaining the optical theorem in the quasiclassical limit.
Since the Aharonov-Bohm effect is the purely quantum effect that has no analogues in classical physics, its persistence in the quasiclassical limit seems to be hardly possible. Nevertheless, we show that the scattering Aharonov-Bohm effect does persist in the quasiclassical limit owing to the diffraction, i.e. the Fraunhofer diffraction in the case when space outside the enclosed magnetic flux is Euclidean, and the Fresnel diffraction in the case when the outer space is conical. Hence, the enclosed magnetic flux can serve as a gate for the propagation of short-wavelength, almost classical, particles. In the case of conical space, this quasiclassical effect which is in principle detectable depends on the particle spin.
Quantum-mechanical scattering of nonrelativistic charged particles by a magnetic vortex of nonzero transverse size is considered. The high-frequency limit of a scattered particle corresponds to the quasiclassical limit, and we show that the scattering Aharonov-Bohm effect persists in the quasiclassical limit owing to the Fraunhofer diffraction in the forward direction. Therefore, the flux of a magnetic vortex serves as a gate for the propagation of quasiclassical particles moving orthogonally to the vortex. The issue of the experimental detection of the Fraunhofer diffraction peak and the scattering Aharonov-Bohm effect is discussed.
Quantum-mechanical scattering of coherent high-energy charged particles by a magnetic vortex is considered. The vortex core is assumed to be impermeable to scattered particles, and effects of its transverse size are taken into account. The limit of high energies of scattered particles corresponds to the quasiclassical limit, and we show that in the scattering the Aharonov-Bohm effect persists in this limit owing to the Fraunhofer diffraction in the forward direction. The issue of the experimental detection of the Fraunhofer diffraction peak and the Aharonov-Bohm effect in the quasiclassical limit is discussed.
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.