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no. 3
An example of resonance instability
Jean-François Bony1; Setsuro Fujiié2; Thierry Ramond3; Maher Zerzeri4
1 IMB, CNRS (UMR 5251), Université de Bordeaux, 33405 Talence, France
2 Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, 525-8577 Japan
3 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France
4 Université Sorbonne Paris-Nord, LAGA, CNRS (UMR 7539), 93430 Villetaneuse, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 3, pp. 535-554.

We construct a semiclassical Schrödinger operator such that the imaginary part of its resonances closest to the real axis changes by a term of size h when a real compactly supported potential of size o(h) is added.

On construit un opérateur de Schrödinger semiclassique dont la partie imaginaire des résonances les plus proches de l’axe réel est modifiée par un terme d’ordre h lorsqu’un potentiel réel à support compact de taille o(h) lui est ajouté.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1743
Classification: 35B34, 35B35, 81Q20, 37C25, 35J10, 35P20
Keywords: Resonances, semiclassical asymptotics, microlocal analysis, spectral instability, Schrödinger operators

Jean-François Bony 1; Setsuro Fujiié 2; Thierry Ramond 3; Maher Zerzeri 4

1 IMB, CNRS (UMR 5251), Université de Bordeaux, 33405 Talence, France
2 Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, 525-8577 Japan
3 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France
4 Université Sorbonne Paris-Nord, LAGA, CNRS (UMR 7539), 93430 Villetaneuse, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Jean-François Bony; Setsuro Fujiié; Thierry Ramond; Maher Zerzeri. An example of resonance instability. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 3, pp. 535-554. doi : 10.5802/afst.1743. https://afst.centre-mersenne.org/articles/10.5802/afst.1743/

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