Unbounded generators of dynamical semigroups

verfasst von

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.

Organisationseinheit(en)

Abt. Nanostrukturen
Institut für Theoretische Physik
SFB 1227: Designte Quantenzustände der Materie (DQ-mat)

Typ

Artikel

Journal

Open Sys. Inf. Dyn.

Band

24

Anzahl der Seiten

1

Publikationsdatum

30.11.2017

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Statistische und nichtlineare Physik, Statistik und Wahrscheinlichkeit, Mathematische Physik

Elektronische Version(en)

https://doi.org/10.1142/S1230161217400157 (Zugang: Unbekannt)