Perturbations of embedded eigenvalues of asymptotically periodic magnetic Schrödinger operators on a cylinder
(2025) In Journal of Mathematical Physics 66(9).- Abstract
We investigate the persistence of embedded eigenvalues for a class of magnetic Laplacians on an infinite cylindrical domain. The magnetic potential is assumed to be C2 and asymptotically periodic along the unbounded direction of the cylinder, with an algebraic decay rate toward a periodic background potential. Under the condition that the embedded eigenvalue of the unperturbed operator lies away from the thresholds of the continuous spectrum, we show that the set of nearby potentials for which the embedded eigenvalue persists forms a smooth manifold of finite and even codimension. The proof employs tools from Floquet theory, exponential dichotomies, and Lyapunov-Schmidt reduction. Additionally, we give an example of a... (More)
We investigate the persistence of embedded eigenvalues for a class of magnetic Laplacians on an infinite cylindrical domain. The magnetic potential is assumed to be C2 and asymptotically periodic along the unbounded direction of the cylinder, with an algebraic decay rate toward a periodic background potential. Under the condition that the embedded eigenvalue of the unperturbed operator lies away from the thresholds of the continuous spectrum, we show that the set of nearby potentials for which the embedded eigenvalue persists forms a smooth manifold of finite and even codimension. The proof employs tools from Floquet theory, exponential dichotomies, and Lyapunov-Schmidt reduction. Additionally, we give an example of a potential which satisfies the assumptions of our main theorem.
(Less)
- author
- Jansen, Jonas LU ; Maad Sasane, Sara LU and Treschow, Wilhelm LU
- organization
-
- Partial differential equations (research group)
- Biomedical Modelling and Computation (research group)
- eSSENCE: The e-Science Collaboration
- ELLIIT: the Linköping-Lund initiative on IT and mobile communication
- LTH Profile Area: AI and Digitalization
- Algebra, Analysis and Dynamical Systems (research group)
- publishing date
- 2025-09
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Physics
- volume
- 66
- issue
- 9
- article number
- 092102
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- scopus:105015175301
- ISSN
- 0022-2488
- DOI
- 10.1063/5.0266328
- language
- English
- LU publication?
- yes
- id
- 26285362-bf40-4afd-97e4-f000fccc634c
- date added to LUP
- 2025-10-16 11:03:03
- date last changed
- 2025-10-16 11:04:03
@article{26285362-bf40-4afd-97e4-f000fccc634c,
abstract = {{<p>We investigate the persistence of embedded eigenvalues for a class of magnetic Laplacians on an infinite cylindrical domain. The magnetic potential is assumed to be C<sup>2</sup> and asymptotically periodic along the unbounded direction of the cylinder, with an algebraic decay rate toward a periodic background potential. Under the condition that the embedded eigenvalue of the unperturbed operator lies away from the thresholds of the continuous spectrum, we show that the set of nearby potentials for which the embedded eigenvalue persists forms a smooth manifold of finite and even codimension. The proof employs tools from Floquet theory, exponential dichotomies, and Lyapunov-Schmidt reduction. Additionally, we give an example of a potential which satisfies the assumptions of our main theorem.</p>}},
author = {{Jansen, Jonas and Maad Sasane, Sara and Treschow, Wilhelm}},
issn = {{0022-2488}},
language = {{eng}},
number = {{9}},
publisher = {{American Institute of Physics (AIP)}},
series = {{Journal of Mathematical Physics}},
title = {{Perturbations of embedded eigenvalues of asymptotically periodic magnetic Schrödinger operators on a cylinder}},
url = {{http://dx.doi.org/10.1063/5.0266328}},
doi = {{10.1063/5.0266328}},
volume = {{66}},
year = {{2025}},
}