Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder
(2017) In Journal of Mathematical Physics 58(1). 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 C^{2} 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,... (More)
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 C^{2} 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.
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 author
 Laptev, Ari and Sasane, Sara Maad ^{LU}
 organization
 publishing date
 20170101
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Mathematical Physics
 volume
 58
 issue
 1
 publisher
 American Institute of Physics
 external identifiers

 scopus:85011297905
 wos:000395279200018
 ISSN
 00222488
 DOI
 10.1063/1.4974360
 language
 English
 LU publication?
 yes
 id
 a6c7b57ff27c4a318ed919b552134678
 date added to LUP
 20170216 06:59:17
 date last changed
 20180107 11:50:09
@article{a6c7b57ff27c4a318ed919b552134678, abstract = {<p>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 C<sup>2</sup> 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.</p>}, articleno = {012105}, author = {Laptev, Ari and Sasane, Sara Maad}, issn = {00222488}, language = {eng}, month = {01}, number = {1}, publisher = {American Institute of Physics}, series = {Journal of Mathematical Physics}, title = {Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder}, url = {http://dx.doi.org/10.1063/1.4974360}, volume = {58}, year = {2017}, }