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 us to apply a suitable transversality theorem.
On the conicity of eigenvalues intersections for parameter-dependent self-adjoint operators / Chittaro, F. C.; Mason, P. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 61:5(2020). [10.1063/1.5115576]
On the conicity of eigenvalues intersections for parameter-dependent self-adjoint operators
Chittaro F. C.;
2020-01-01
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 us to apply a suitable transversality theorem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
