Proposition for a PhD Thesis: Integrability techniques in the dynamics of spins particles and applications to optimal control

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 5584

Institut 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

E-mail
 Bernard Bonnard (Supervisor)  bernard.bonnard@u-bourgogne.fr
Thierry Combot (Co-Supervisor)  thierry.combot@u-bourgogne.fr

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.