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# Documents  81Q12 | enregistrements trouvés : 3

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## Spectral theory and semi-classical analysis for the complex Schrödinger operator Helffer, Bernard | CIRM H

Post-edited

Research talks;Partial Differential Equations;Mathematical Physics

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. 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, ...

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## Non-selfadjoint operators in quantum physics: mathematical aspects Bagarello, Fabio ; Gazeau, Jean-Pierre ; Szafraniec, Franciszek Hugon ; Znojil, Miloslav | Wiley 2015

Ouvrage

- xxiv; 407 p.
ISBN 978-1-118-85528-7

Localisation : Ouvrage RdC (NON)

physique quantique # opérateur non-adjoint # mécanique quantique # symétrie CPT # espace de Krein # théorie de la perturbation # physique nucléaire # physique des particules # physique de la matière condensée

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## Mathematical theory of scattering resonances Dyatlov, Semyon ; Zworski , Maciej | American Mathematical Society 2019

Ouvrage

- xi; 634 p.
ISBN 978-1-4704-4366-5

Graduate studies in mathematics , 0200

Localisation : Collection 1er étage

résonance # dispersion # oscillation # fréquence des oscillations # physique mathématique # prolongement méromorphe # théorie spectrale # valeurs propres # théorie quantique

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