Optimal bilinear control of Gross-Pitaevskii equations

Autor:	Hintermüller, Michael, Marahrens, Daniel, Markowich, Peter A., Sparber, Christof
Rok vydání:	2012
Předmět:	Mathematics - Optimization and Control Condensed Matter - Quantum Gases Mathematics - Analysis of PDEs 49J20 (Primary) 81Q93 49J50 (Secondary)
Druh dokumentu:	Working Paper
Popis:	A mathematical framework for optimal bilinear control of nonlinear Schr\"odinger equations of Gross-Pitaevskii type arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier efforts found in the literature in several aspects. In particular, the cost induced by the physical work load over the control process is taken into account rather then often used $L^2$- or $H^1$-norms for the cost of the control action. Well-posedness of the problem and existence of an optimal control is proven. In addition, the first order optimality system is rigorously derived. Also a numerical solution method is proposed, which is based on a Newton type iteration, and used to solve several coherent quantum control problems. Comment: 30 pages, 14 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1202.2306 Zobrazit plný text záznamu View this record from Arxiv