# On singular perturbations of quantum dynamical semigroups

## TL;DR

This paper investigates singular perturbations of quantum dynamical semigroups, providing new examples and generalizations that address existing conjectures and simplify previous constructions.

## Contribution

It introduces new examples of singular perturbations, generalizes previous models to answer Arveson's conjecture, and simplifies the construction of nonstandard dynamical semigroups.

## Key findings

- Provided a positive answer to Arveson's conjecture
- Developed a generalized example of dynamical semigroups
- Simplified the construction of nonstandard dynamical semigroups

## Abstract

We consider two examples of dynamical semigroups obtained by singular perturbations of a standard generator which are special case of unbounded completely positive perturbations studied in detail in [10]. In the section 2 we propose a generalization of an example from [1] aimed to give a positive answer to a conjecture of Arveson. In the section 3 we consider in greater detail an improved and simplified construction of a nonstandard dynamical semigroup outlined in our short communication [13].