On the optimal control of a Kohn-Sham quantum model скачать в хорошем качестве

On the optimal control of a Kohn-Sham quantum model

By Alfio Borzi (Institut für Mathematik, Universität Würzburg, Germany) Abstract: A Kohn-Sham (KS) model is a system of nonlinear coupled Schrödinger equations that describe multi-particle quantum systems in the framework of the time-dependent density functional theory. In this talk, existence, uniqueness and regularity of solutions to a time-dependent Kohn-Sham model are investigated. Further, in view of control applications, the presence of a control function and of an inhomogeneity are also considered. With this preparation, an optimal control of many-electron systems is formulated where the purpose of the control is to track a desired trajectory of the electronic density and to achieve a desired target configuration. The theory and numerical solution of the resulting KS optimal control problem are discussed. Results of numerical experiments successfully validate the proposed control framework. ---------------------------------- Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75005 PARIS http://www.ihp.fr/