Regular propagators of bilinear quantum systems

摘要

The present analysis deals with the regularity of solutions of bilinear control systems of the type x' = (A + u(t)B)x where the state x belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators A and B are skew-adjoint and the control u is a real valued function. Such systems arise, for instance, in quantum control with the bilinear Schrodinger equation. For the sake of the regularity analysis, we consider a more general framework where A and B are generators of contraction semigroups.