On singular perturbations of quantum dynamical semigroups

We consider two examples of quantum dynamical semigroups obtained by singular perturbations of a standard generator which are special case of unbounded completely positive perturbations studied in detail in [11]. In Sec. 2, we propose a generalization of an example in [15] aimed to give a positive answer to a conjecture of Arveson. In Sec. 3 we consider in greater detail an improved and simplified construction of a nonstandard dynamical semigroup outlined in our short communication [12].