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Resonance of minimizers for n-level quantum systems with an arbitrary cost

Ugo Boscain, Grégoire Charlot (2004)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an optimal control problem describing a laser-induced population transfer on a n -level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for n = 2 and n = 3 ): instead of looking...

Resonance of minimizers for n-level quantum systems with an arbitrary cost

Ugo Boscain, Grégoire Charlot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an optimal control problem describing a laser-induced population transfer on a n-level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for n=2 and n=3): instead...

Results on existence of solution for an optimal design problem.

Carmen Calvo Jurado, Juan Casado Díaz (2003)

Extracta Mathematicae

In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

Liana Cioban, Ernö Csetnek (2013)

Open Mathematics

Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...

Rigidity for the hyperbolic Monge-Ampère equation

Chun-Chi Lin (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Some properties of nonlinear partial differential equations are naturally associated with the geometry of sets in the space of matrices. In this paper we consider the model case when the compact set  K is contained in the hyperboloid ℋ - 1 , where ℋ - 1 ⊂ 𝕄 sym 2 × 2 , the set of symmetric 2 × 2 matrices. The hyperboloid ℋ - 1 is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampère equation det ∇ 2 u = - 1 . For some compact subsets K ⊂ ℋ - 1 containing a rank-one connection, we show the rigidity property of K by imposing...

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