Spectral theory and semi-classical analysis for the complex Schrödinger operator | Vidéo | Carmin.tv

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Spectral theory and semi-classical analysis for the complex Schrödinger operator

By Bernard Helffer

Appears in collection : Mathematical aspects of physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints

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.

Information about the video

Date of recording 07/06/2017
Date of publication 15/06/2017
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19180803
Cite this video Helffer, Bernard (07/06/2017). Spectral theory and semi-classical analysis for the complex Schrödinger operator. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19180803
URL https://dx.doi.org/10.24350/CIRM.V.19180803

Domain(s)

Bibliography

Almog, Y., Grebenkov, D., & Helffer, B. (2017). On a Schrödinger operator with a purely imaginary potential in the semiclassical limit. <arXiv:1703.07733> - https://arxiv.org/abs/1703.07733

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