On perturbations of dynamical semigroups defined by covariant completely positive measures on the semi-axis

TL;DR

This paper studies how dynamical semigroups in quantum mechanics are affected by covariant completely positive measures, introducing unbounded perturbations and applying them to construct specific quantum flows.

Contribution

It introduces a new method for perturbing dynamical semigroups using unbounded linear perturbations of generators, with applications to quantum flows.

Findings

Constructed perturbations of semigroups via unbounded generators.

Applied the method to generate a flow of shifts in quantum systems.

Extended the theory to non-unital *-endomorphisms on CAR algebra.

Abstract

We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is based upon unbounded linear perturbations of generators of the preadjoint semigroups on the space of nuclear operators. As an application we construct a perturbation of the semigroup of non-unital *-endomorphisms on the algebra of canonical anticommutation relations resulting in the flow of shifts.