Non-Conservative Minimal Quantum Dynamical Semigroups

TL;DR

This paper establishes criteria for non-conservativity in minimal quantum dynamical semigroups, linking the problem to von Neumann's defect indices, and extends existing conservativity criteria.

Contribution

It provides necessary and sufficient conditions for non-conservativity of minimal quantum dynamical semigroups and relates these conditions to von Neumann defect indices.

Findings

Criteria for non-conservativity are established.

Connections between conservativity and von Neumann defect indices are demonstrated.

Extensions of known conservativity criteria are presented.

Abstract

We give necessary and sufficient conditions for non-conservativity of a class of minimal quantum dynamical semigroups (qds). We extend some well known criteria for conservativity of minimal qds and show interesting relations of the conservativity problem with the von Neumann theory of the defect indices of a symmetric closed operator.