Mathematics and Applications
Doctorate School Carnot-Pasteur (http://ed-carnot-pasteur.u-bourgogne.fr/)
Proposition: subject for a PhD thesis (submitted April 2014)
Title: Integrability techniques in the dynamics of spins particles and applications to optimal control
Research Unit: Mathematics Institue of Burgundy (http://math.u-bourgogne.fr/): IMB, UMR 5584Institut de Mathématiques de Bourgogne – UMR 5584 CNRS Université de Bourgogne Faculté des Sciences Mirande 9 avenue Alain Savary, BP 47870 21078 Dijon Cedex
Thesis supervisor and co-supervisor:
Name, First name
|Bernard Bonnard (Supervisor)||email@example.com|
|Thierry Combot (Co-Supervisor)||firstname.lastname@example.org|
Main scientific domain of the PhD: Mathematics and Applications
Secondary scientific domain of the PhD: Spin dynamics and applications to quantum computing
Scientific Project Description:
Dynamics of controlled spins in NMR has applications in medical imaging and quantum computing. The Maximum Principle leads to the study of Hamiltonian systems. A preliminary step is to compute first integrals and to characterize integrability properties. We are then interested to study the following objects related to the optimality of the solutions: geometric calculation of conjugate and cut loci.
Required knowledge and skills: Knowledge in dynamical systems and optimal control.