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

Francesca Chittaro (1) , Paolo Mason (2)

1 CDE - Contrôle et Diagnostic pour l’Environnement
2 L2S - Laboratoire des signaux et systèmes

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.

Domaines: Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]

Francesca Chittaro, Paolo Mason. On the conicity of eigenvalues intersections for parameter-dependent self-adjoint operators. Journal of Mathematical Physics, 2020, 61 (5), ⟨10.1063/1.5115576⟩. ⟨hal-02160192v2⟩