Magnetic Neumann problems with Aharonov-Bohm potentials: boundary asymptotics of eigenvalues and splitting phenomena
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918340269703168 |
|---|---|
| author | Felli, Veronica Roychowdhury, Prasun Siclari, Giovanni |
| author_facet | Felli, Veronica Roychowdhury, Prasun Siclari, Giovanni |
| contents | We study a planar magnetic Schrödinger operator with an Aharonov-Bohm vector potential, under Neumann boundary conditions. Through a gauge transformation, the corresponding eigenvalue problem can be formulated in terms of the Laplacian on a fractured domain, where the fracture lies along the segment connecting the pole to its projection on the boundary. As the pole approaches the boundary, we prove that the eigenvalues converge to those of the Neumann Laplacian and the variation exhibits a logarithmic vanishing rate. In the case of multiple eigenvalues, when the pole approaches a fixed point of the boundary, we observe a splitting phenomenon, with the largest branch separating from the others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14522 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Magnetic Neumann problems with Aharonov-Bohm potentials: boundary asymptotics of eigenvalues and splitting phenomena Felli, Veronica Roychowdhury, Prasun Siclari, Giovanni Analysis of PDEs 35J10, 35P20, 35J75 We study a planar magnetic Schrödinger operator with an Aharonov-Bohm vector potential, under Neumann boundary conditions. Through a gauge transformation, the corresponding eigenvalue problem can be formulated in terms of the Laplacian on a fractured domain, where the fracture lies along the segment connecting the pole to its projection on the boundary. As the pole approaches the boundary, we prove that the eigenvalues converge to those of the Neumann Laplacian and the variation exhibits a logarithmic vanishing rate. In the case of multiple eigenvalues, when the pole approaches a fixed point of the boundary, we observe a splitting phenomenon, with the largest branch separating from the others. |
| title | Magnetic Neumann problems with Aharonov-Bohm potentials: boundary asymptotics of eigenvalues and splitting phenomena |
| topic | Analysis of PDEs 35J10, 35P20, 35J75 |
| url | https://arxiv.org/abs/2602.14522 |