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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 : Thursday, May 14, 2020 - 8:34:38 AM
Last modification on : Saturday, November 14, 2020 - 1:00:02 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), 2020, 61 (5), ⟨10.1063/1.5115576⟩. ⟨hal-02160192v2⟩

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