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ID 53917
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Author
Tamura, Hideo
Abstract
We study the Aharonov–Bohm effect (AB effect) in quantum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact support, which are largely separated from one another. The obstacles by which the magnetic fields are completely shielded are horizontally placed between the supports of the two potentials. The fields do not influence particles from a classical mechanical point of view, but quantum particles are influenced by the corresponding vector potential which does not necessarily vanish outside the obstacle. This quantum phenomenon is called the AB effect. The resonances are shown to be generated near the real axis by the trajectories trapped between two supports of the scalar potentials as the distances between the scatterers go to infinity. We analyze how the AB effect influences the location of resonances. The result is described in terms of the backward amplitudes for scattering by each of the scalar potentials, and it depends heavily on the ratios of the distances between the four scatterers as well as on the magnetic fluxes of the fields.
Keywords
Aharonov–Bohm effect
magnetic Schrödinger operator
resonances
Published Date
2016-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume58
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
41
End Page
78
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2016 by the Editorial Board of Mathematical Journal of Okayama University
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publisher
Refereed
True
Submission Path
mjou/vol58/iss1/2
JaLCDOI