Regular propagators of bilinear quantum systems

Regular propagators of bilinear quantum systems

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 in nite 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 Schrödinger equation...

On the controllability of bilinear quantum systems

Periodic excitations of bilinear quantum systems

A well-known method of transferring the population of a quantum system from an eigenspace of the free Hamiltonian to another is to use a periodic control law with an angular frequency equal to the difference of the eigenvalues. For finite dimensional quantum systems, the classical theory of averaging provides a rigorous explanation of this experimentally validated result. This paper extends thi...

Controllable quantities for bilinear quantum systems

Nonperturbative propagators in quantum chromodynamics.

Leading nonperturbative corrections to the quark and gluon propagators are derived following the assumption that the nonperturbative QCD vacuum can be described in terms of non-vanishing vacuum expectation values for the composite operators [T&I and [GEY]. Th e nonperturbative quark propagator can be described in terms of a running quark mass and a running normalization function. These quantiti...