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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02160192
Contributor : Francesca Carlotta Chittaro <>
Submitted on : Wednesday, June 19, 2019 - 1:47:55 PM
Last modification on : Friday, May 29, 2020 - 3:03:53 AM

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Francesca Chittaro, Paolo Mason. On the conicity of eigenvalues intersections for parameter-dependent self-adjoint operators. Journal of Mathematical Physics, American Institute of Physics (AIP), In press, 61 (5). ⟨hal-02160192v1⟩

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