Perturbations of embedded eigenvalues for a magnetic Schrodinger operator on a cylinder
File(s)
Accepted version
Author(s)
Laptev, A
Sasane, SM
Type
Journal Article
Abstract
Perturbation problems for operators with embedded eigenvalues are generally challenging since the embedded eigenvalues cannot be separated from the rest of the spectrum. In this paper, we study a perturbation problem for embedded eigenvalues for a magnetic Schrödinger operator, when the underlying domain is a cylinder. The magnetic potential is C2 with an algebraic decay rate as the unbounded variable of the cylinder tends to ±∞. In particular, no analyticity of the magnetic potential is assumed. We also assume that the embedded eigenvalue of the unperturbed problem is not the square of an integer, thus avoiding the thresholds of the continuous spectrum of the unperturbed operator. We show that the set of nearby potentials, for which a simple embedded eigenvalue persists, forms a smooth manifold of finite codimension.
Date Issued
2017-01-31
Date Acceptance
2017-01-09
Citation
Journal of Mathematical Physics, 2017, 58 (1)
ISSN
0022-2488
Publisher
AIP Publishing
Journal / Book Title
Journal of Mathematical Physics
Volume
58
Issue
1
Copyright Statement
© 2017 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Ari Laptev and Sara Maad Sasane, Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder, Journal of Mathematical Physics 58, 012105 (2017); doi: http://dx.doi.org/10.1063/1.4974360 and may be found at https://dx.doi.org/10.1063/1.4974360
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000395279200018&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Physics, Mathematical
Physics
PSEUDO-LAPLACIANS
BILAPLACIAN
POTENTIALS
SPECTRUM
01 Mathematical Sciences
02 Physical Sciences
Mathematical Physics
Publication Status
Published
Article Number
ARTN 012105