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ID 53918
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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 vertically placed between the supports of the two potentials. The system yields a two dimensional model of a toroidal scattering system in three dimensions. 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 heavily depends on the width between the two obstacles as well as on the magnetic fluxes. The critical case is that the width is comparable to the square root of the distance between the supports of the two potentials.
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
79
End Page
108
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
File Version
publisher
Refereed
True
Submission Path
mjou/vol58/iss1/3