Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator [14]. For bilinear quantum control problems, no general results are available to fully determine when this mapping is singular or not. In this paper we give sufficient conditions, in terms of elements of the evolution semigroup, for a traje...

We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family inner products, also providing new information on order extreme points in some previously studied cases.

Let Ω be a convex domain with smooth boundary in Rd. It has been shown recently that the semigroup generated by the discrete Laplacian for quasi-uniform families of piecewise linear finite element spaces on Ω is analytic with respect to the maximum-norm, uniformly in the mesh-width. This implies a resolvent estimate of standard form in the maximum-norm outside some sector in the right halfplane...

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

The inner-outer part factorisation of analytic representations in the unit disk is used for an effective characterisation of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorisation is intimately connected to the number-phase Weyl semigroup and its properties. In the Barut-Girardello analytic representation the factorisation is implemented as ...

Let V be a finite dimensional vector space. Given a decomposition V ⊗ V = ⊕i Ii, define n quadratic algebras (V, Jm) where Jm = ⊕i6=mIi. This decomposition defines also the quantum semigroup M(V ; I1, ..., In) which acts on all these quadratic algebras. With the decomposition we associate a family of associative algebras Ak = Ak(I1, ...In), k ≥ 2. In the classical case, when V ⊗ V decomposes in...