# F. Albertini's research while affiliated with Centro di Ricerca in Matematica Pura ed Applicata and other places

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## Publications (8)

Using Lagrangian formalism, switching electrical networks can be modeled as systems varying on Lie groups which evolve according to a finite number of vector fields. In particular, under appropriate assumptions, LC circuits can be modeled as systems on SO(n), The first goal of this report is to formalize the modeling of LC circuits as systems on SO...

In this paper, we study the observability properties of quantum systems and the related problem of parameter identification with particular emphasys on networks of spin 1/2 particles. These networks model magnetic molecules. We give criteria for observability of general quantum systems and apply these to characterize the equivalence classes of spin...

In this note, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability.

In this paper, we study the controllability properties and the Lie algebra structure of networks of particles with spin immersed in an electro-magnetic field. We relate the Lie algebra structure to the properties of a graph whose nodes represent the particles and an edge connects two nodes if and only if the interaction between the two correspondin...

In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability. The pa...

In this paper, we define three different notions of
controllability for quantum mechanical systems involving the possibility
of driving the evolution operator as well as the state of the system. By
using general results on transitivity of transformation groups on
spheres we establish the connections among these different notions of
controllability....

In this paper, we provide a complete analysis of the Lie algebra
structure of a system of n interacting spin ½ particles with
different gyromagnetic ratios in an electro-magnetic field. We relate
the structure of this Lie algebra to the properties of a graph whose
nodes represent the particles and an edge connects two nodes if and only
if th...

In this paper, we provide a complete analysis of the Lie algebra structure of a system of n interacting spin ½ particles with different gyromagnetic ratios in an electro-magnetic field. We relate the structure of this Lie algebra to the properties of a graph whose nodes represent the particles and an edge connects two nodes if and only if the inter...

## Citations

... Lie theoretical techniques provide a powerful tool to characterise the expressibility of quantum controllable systems [70]. They have been previously used in the literature to prove the universality of a set of protocols under certain assumptions [39]. ...

... In [10,11] electrical lumped devices and electromechanical systems are described using Lagrange and Hamilton formalism with and without losses, whereas the generalized motion in Riemannian space, i.e. non-Euclidian, is considered. Further investigations on Lagrangians for lumped RLC-circuits are presented, for instance, in [12][13][14], and nonlinear, lumped RLC networks are described in [15,16]. ...

... [10]. We only notice that the system is easily seen to be observable as soon as it is controllable [3] but that due to the complicated structure of S, linear state observers are inadequate (they do not preserve ̺ ). In the heteronuclear case, the estimation of ̺ α and ̺ β is an easier task than in the homonuclear one. ...

Reference: Feedback Control of Spin Systems

... De nombreux problèmes consistent à déterminer un champ laser qui permet d'amener le système de son état initial vers un état proche d'un état cible donné ou d'une classe d'états spécifiques, par exemple maximisant la valeur d'une observable. Avant d'aborder ce problème, il faut dégager des critères de contrôlabilté de l'équation de Schrödinger (voir par exmeple [38,39,40,41,42,43] et [50] pour une discussion plus générale), ce qui consiste à étudier si, pour tout couple (ψ 0 , ψ cible ) ∈ (S N (0, 1)) 2 , il existe un temps final T > 0 et une impulsion laser ε(t) ∈ L 2 ([0, T ]; R) tels que le système partant de ψ(t = 0) = ψ 0 vérifie ψ(t = T ) = ψ cible . Si cette condition est remplie le système est dit contrôlable. ...

... When restricting to pure states in even dimensions N , it suffices that the system Lie algebra yields the Lie algebra of all unitary symplectic matrices of dimension N . Otherwise, in finite dimensional closed systems, pure-state controllability, mixedstate controllability, and full unitary gate controllability coincide [15,191,356]. In infinite dimensions, the situation is more involved and in spite of recent progress elucidated in Sect. ...

... On the other hand, from a practical standpoint, it is of much importance to control quantum states in order to create entangled states. Many of papers on control problems for multiqubit systems deal with control systems on unitary groups1235,6,15161723]. The theory of control on compact Lie groups has been established [14] . ...