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ID 41395
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Abstract
The Aharonov–Bohm Hamiltonian is the energy operator which governs quantum particles moving in a solenoidal field in two dimensions. We analyze asymptotic properties of its Green function with spectral parameters in the unphysical sheet. As an application, we discuss the lower bound on resonance widths for scattering by two magnetic fields with compact supports at large separation. The bound is evaluated in terms of backward scattering amplitudes by a single magnetic field. A special emphasis is placed on analyzing how a trajectory oscillating between two magnetic fields gives rise to resonances near the real axis, as the distance between two supports goes to infinity. We also refer to the relation to the semiclassical resonance theory for scattering by two solenoidal fields.
Keywords
Aharonov-Bohm Hamiltonian
Green function
magnetic Schrödinger operator
scattering amplitude
resonance width
Published Date
2011-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume53
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
1
End Page
37
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol53/iss1/1
JaLCDOI