CONTROLLABILITY OF BILINEAR QUANTUM SYSTEMS 

Bilinear control systems accessibility and controllability properties; bilinear systems and matrix transition Lie groups; structure of matrix Lie groups (homogeneous spaces, transitivity, lifting of vector fields, linear and affine structure)  Lie algebras (semisimpicity, Cartan criteria, structure theory); examples: rigid bodies on SO(3) and SE(3);

Application: quantum bilinear control systems finite dimensional Schrodinger equation; quantum Markovian master equation; example: two level system