Unbounded generators of dynamical semigroups

authored by

Inken Siemon, Alexander S. Holevo, Reinhard F. Werner

Abstract

Dynamical semigroups have become the key structure for describing open system dynamics in all of physics. Bounded generators are known to be of a standard form, due to Gorini, Kossakowski, Sudarshan and Lindblad. This form is often used also in the unbounded case, but rather little is known about the general form of unbounded generators. In this paper we first give a precise description of the standard form in the unbounded case, emphasizing intuition, and collecting and even proving the basic results around it. We also give a cautionary example showing that the standard form must not be read too naively. Further examples are given of semigroups, which appear to be probability preserving to first order, but are not for finite times. Based on these, we construct examples of generators which are not of standard form.

Organisation(s)

Nanostructures Section
Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)

Type

Article

Journal

Open Sys. Inf. Dyn.

Volume

24

No. of pages

1

Publication date

30.11.2017

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics, Statistics and Probability, Mathematical Physics

Electronic version(s)

https://doi.org/10.1142/S1230161217400157 (Access: Unknown)