0000000000776718
AUTHOR
Grégoire Charlot
showing 3 related works from this author
Optimal control of the Schrödinger equation with two or three levels
2007
In this paper, we present how techniques of “control theory”, “sub-Riemannian geometry” and “singular Riemannian geometry” can be applied to some classical problems of quantum mechanics and yield improvements to some previous results.
On stability of generic subriemannian caustic in the three-space
2000
Abstract The singularities of exponential mappings in subriemannian geometry are interesting objects, that are already non-trivial at the local level, contrarily to their Riemannian analogs. The simplest case is the three-dimensional contact case. Here we show that the corresponding generic caustics have moduli at the origin, and the first module that occurs has a simple geometric interpretation. On the contrary, we prove a stability result of the “big wave front”, that is, of the graph of the multivalued arclength function, reparametrized in a certain way. This object is a three-dimensional surface, which has also the natural structure of a wave front. The projection on the three-dimension…
Resonance of minimizers forn-level quantum systems with an arbitrary cost
2004
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 for minimizers on the sphere one is reduced to look just for minimizers on the sphere . Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal mi…