2003/08/20 by Ugo Boscain, Boscain, Ugo, Gregoire Charlot +2 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Biology Tumor Growth #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0308103
The part about abnormal extremals is now given in a weaker form, following a remark of an anonymous referee
openalex publication_date 2003/08/20 · arxiv created 2004/01/13 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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 S2n-1⊂\Cn one is reduced to look just for minimizers on the sphere Sn-1⊂ \Rn. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer.