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On the conicity of eigenvalues intersections for parameter-dependent self-adjoint operators

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  • Additional Information
    • Contributors:
      Contrôle et Diagnostic pour l’Environnement (CDE); Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon) (LIS); Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS); Laboratoire des signaux et systèmes (L2S); Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS); Fondation Sciences Mathématiques de Paris(FSMP) CARTT – IUT de Toulon.; ANR-17-CE40-0007,QUACO,Contrôle quantique : systèmes d'EDPs et applications à l'IRM(2017)
    • Publication Information:
      HAL CCSD
      American Institute of Physics (AIP)
    • Publication Date:
      2020
    • Collection:
      Université de Toulon: HAL
    • Abstract:
      International audience ; Motivated by recent controllability results for the bilinear Schrödinger equation based on the existence of conical intersections, in this paper we identify two physically interesting families of parameter-dependent Hamiltonians that admit residual and prevalent subfamilies for which all double eigenvalues are conical. In order to obtain such a result we exploit a characterization of conical intersections in terms of a transversality condition which allows to apply a suitable transversality theorem.
    • Relation:
      hal-02160192; https://hal.science/hal-02160192; https://hal.science/hal-02160192v2/document; https://hal.science/hal-02160192v2/file/JMP19-AR-00920.pdf
    • Accession Number:
      10.1063/1.5115576
    • Online Access:
      https://doi.org/10.1063/1.5115576
      https://hal.science/hal-02160192
      https://hal.science/hal-02160192v2/document
      https://hal.science/hal-02160192v2/file/JMP19-AR-00920.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.E5E02BE3