Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators

TL;DR

This paper investigates the construction and conservativity of quantum dynamical semigroups generated by noncommutative unbounded elliptic operators, extending the understanding of Lindblad-type generators in quantum dynamics.

Contribution

It introduces a method to construct minimal quantum dynamical semigroups from noncommutative unbounded elliptic operators and verifies their conservativity using Chebotarev and Fagnola's criteria.

Findings

Successfully constructed minimal quantum dynamical semigroups

Proved semigroups are conservative under certain conditions

Extended the class of generators for quantum dynamical semigroups

Abstract

We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola's sufficient conditions for conservativity to show that the semigroups are conservative.