Group Theoretical Approach for Controlled Quantum Mechanical Systems

The aim of this research is the study of controllability of quantum mechanical systems and feedback control of de-coherence in order to gain an insight on the structure of control of quantum systems. During the reporting period, many important results have been obtained. Particularly, we have obtained results on 1 Controllability of quantum systems possesses infinite-dimensional system Lie-algebra, and 2 Feedback control of de-coherence in open quantum systems. Algebraic conditions for controllability and the control of de-coherences were obtained. To our knowledge no such conditions existed in the literature for quantum mechanical systems. The obtained results are very important. They will guide us on how to control a quantum system with scattering states possesses continuous spectrum and help us to design feedback control for quantum systems. Additionally we have published our results in high standard journals and presented our results at prestigious conferences. The PI was invited to give invited and plenary addresses at important control conferences.