|
|||||
 |
|
|
|
|
|
|
|
Semiclassical
eigenvalue estimates under magnetic steps
Wafaa Assaad, Bernard Helffer and Ayman Kachmar |
|
Vol. 17 (2024), No. 2, 535–585
|
 |
Abstract |
|
We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues for the Dirichlet magnetic Laplacian with a nonuniform magnetic field having a jump discontinuity along a smooth curve. The asymptotics hold in the semiclassical limit, which also corresponds to a large magnetic field limit and is valid under a geometric assumption on the curvature of the discontinuity curve. |
Keywords
semiclassical analysis, magnetic Laplacian, magnetic steps
|
Mathematical Subject Classification
Primary: 35P15, 35P20, 81Q20
|
Milestones
Received: 6 September 2021
Revised: 25 March 2022
Accepted: 11 July 2022
Published: 6 March 2024
|
Authors |
| Wafaa Assaad | |
| Faculty of Arts and Sciences Lebanese International University Beirut Lebanon |
|
| Bernard Helffer | |
| Laboratoire de Mathématiques Jean
Leray Université de Nantes Nantes France |
|
| Ayman Kachmar | |
| School of Science and
Engineering The Chinese University of Hong Kong (Shenzhen) Shenzhen China |
|
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
