Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells: Analysis near the bottom
| dc.creator | Helffer, B. | |
| dc.creator | Kordyukov, Y. A. | |
| dc.date | 2008-12-23 | |
| dc.date.accessioned | 2026-07-07T12:21:22Z | |
| dc.date.available | 2026-07-07T12:21:22Z | |
| dc.description | We consider a periodic magnetic Schrödinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a noncompact Riemannian manifold $M$ such that $H^1(M, {\mathbb R})=0$ endowed with a properly discontinuous cocompact isometric action of a discrete group. We assume that there is no electric field and that the magnetic field has a periodic set of compact magnetic wells. We suppose that the magnetic field vanishes regularly on a hypersurface $S$. First, we prove upper and lower estimates for the bottom $λ_0(H^h)$ of the spectrum of the operator $H^h$in $L^2(M)$. Then, assuming the existence of non-degenerate miniwells for the reduced spectral problem on $S$, we prove the existence of an arbitrary large number of spectral gaps for the operator $H^h$ in the region close to $λ_0(H^h)$, as $h\to 0$. In this case, we also obtain upper estimates for the eigenvalues of the one-well problem. | |
| dc.description | 33 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0812.4350 | |
| dc.identifier | http://arxiv.org/abs/0812.4350 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213342 | |
| dc.subject | Spectral Theory | |
| dc.subject | Analysis of PDEs | |
| dc.title | Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells: Analysis near the bottom | |
| dc.type | text |