Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential
| dc.creator | Camus, Brice | |
| dc.date | 2005-02-27 | |
| dc.date.accessioned | 2026-07-07T06:39:29Z | |
| dc.date.available | 2026-07-07T06:39:29Z | |
| dc.description | We study the semi-classical trace formula at a critical energy level for a Schrödinger operator on $\mathbb{R}^{n}$. We assume here that the potential has a totally degenerate critical point associated to a local maximum. The main result, which establishes the contribution of the associated equilibrium in the trace formula, is valid for all time in a compact subset of $\mathbb{R}$ and includes the singularity in $t=0$. For these new contributions the asymptotic expansion involves the logarithm of the parameter $h$. Depending on an explicit arithmetic condition on the dimension and the order of the critical point, this logarithmic contribution can appear in the leading term. | |
| dc.description | 27 pages, perhaps to be revised | |
| dc.identifier | https://arxiv.org/abs/math/0502568 | |
| dc.identifier | http://arxiv.org/abs/math/0502568 | |
| dc.identifier | Journal of Differential Equations. Volume 226, Issue 1 , 1 July 2006, Pages 295-322 | |
| dc.identifier | doi:10.1016/j.jde.2005.10.003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101098 | |
| dc.subject | Spectral Theory | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Classical Physics | |
| dc.title | Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential | |
| dc.type | text |