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Spectral theory and semi-classical analysis for the complex Schrödinger operator
Post-edited
Authors : Helffer, Bernard (Author of the conference)
CIRM (Publisher )
35J10 - Schrödinger operator
35P10 - Completeness of eigenfunctions, eigenfunction expansions for PD operators
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
47A10 - Spectrum and resolvent of linear operators
82D55 - Superconductors
81Q12 - Non-selfadjoint operator theory in quantum theory
CIRM (Publisher )
Abstract :
We consider the operator $\mathcal{A}_h = -h^2 \Delta + iV$ in the semi-classical limit $h \to 0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of $\mathcal{A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, we apply our techniques to the more general Robin boundary condition and to a transmission problem which is of significant interest in physical applications.
MSC Codes : 35J10 - Schrödinger operator
35P10 - Completeness of eigenfunctions, eigenfunction expansions for PD operators
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
47A10 - Spectrum and resolvent of linear operators
82D55 - Superconductors
81Q12 - Non-selfadjoint operator theory in quantum theory
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/06/17 Conference Date : 07/06/17 Subseries : Research talks arXiv category : Spectral Theory ; Mathematical Physics Mathematical Area(s) : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:42:04 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-06-07_Helffer.mp4 
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Information on the Event
Event Title : Mathematical aspects of physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjointsEvent Organizers : Krejcirik, David ; Siegl, Petr Dates : 05/06/17 - 09/06/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1596.html
Citation Data
DOI : 10.24350/CIRM.V.19180803Cite this video as: Helffer, Bernard (2017). Spectral theory and semi-classical analysis for the complex Schrödinger operator. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19180803 URI : http://dx.doi.org/10.24350/CIRM.V.19180803 |
See Also
- [Multi angle] Truncated Toeplitz operators / Author of the conference Câmara, Cristina.
- [Multi angle] A new complex spectrum associated to invisibility in waveguides / Author of the conference Bonnet-Ben Dhia, Anne-Sophie.
- [Multi angle] New spectral bounds for damped systems / Author of the conference Tretter, Christiane.
- [Multi angle] The invariant subspace problem: a concrete operator theory approach / Author of the conference Gallardo-Gutiérrez, Eva A..
Bibliography
- Almog, Y., Grebenkov, D., & Helffer, B. (2017). On a Schrödinger operator with a purely imaginary potential in the semiclassical limit.
