# American Institute of Mathematical Sciences

December  2020, 10(4): 877-911. doi: 10.3934/mcrf.2020023

## Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems

 1 Inria & Université Côte d'Azur, INRA, CNRS, Sorbonne Université, Sophia Antipolis, France 2 CNRS & Sorbonne Université, Inria, Université de Paris, Laboratoire Jacques-Louis Lions, Paris, France 3 Inria & Sorbonne Université, Université de Paris, CNRS, Laboratoire Jacques-Louis Lions, Paris, France

* Corresponding author: Nicolas Augier

Received  August 2019 Revised  January 2020 Published  March 2020

We study one-parametric perturbations of finite dimensional real Hamiltonians depending on two controls, and we show that generically in the space of Hamiltonians, conical intersections of eigenvalues can degenerate into semi-conical intersections of eigenvalues. Then, through the use of normal forms, we study the problem of ensemble controllability between the eigenstates of a generic Hamiltonian.

Citation: Nicolas Augier, Ugo Boscain, Mario Sigalotti. Semi-conical eigenvalue intersections and the ensemble controllability problem for quantum systems. Mathematical Control & Related Fields, 2020, 10 (4) : 877-911. doi: 10.3934/mcrf.2020023
##### References:

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##### References:
Conical intersection as a function of the controls $(u,v)\in {\mathbb{R}}^2$
Semi-conical intersection of eigenvalues as a function of the controls $(u,v)\in {\mathbb{R}}^2$
Semi-conical intersection for the STIRAP as a function of the controls $(u,v)\in {\mathbb{R}}^2$
A curve $(u,v)$ as in the statement of Theorem 1.3
A control path passing at a semi-conical intersection in the non-conical direction as a function of the controls $(u,v)\in {\mathbb{R}}^2$
A graphical representation of condition (C)
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