Advances in Mathematical Physics
Volume 2011 (2011), Article ID 625978, 16 pages
http://dx.doi.org/10.1155/2011/625978
Research Article

Quantum Dynamical Semigroups and Decoherence

Mario Hellmich1,2

1Faculty of Physics, University of Bielefeld, Universitätsstraβe 25, 33615 Bielefeld, Germany
2Bundesamt für Strahlenschutz (Federal Office for Radiation Protection), Willy-Brandt-Straße 5, 38226 Salzgitter, Germany

Received 22 June 2011; Accepted 31 August 2011

Academic Editor: Christian Maes

Copyright © 2011 Mario Hellmich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove a version of the Jacobs-de Leeuw-Glicksberg splitting theorem for weak* continuous one-parameter semigroups on dual Banach spaces. This result is applied to give sufficient conditions for a quantum dynamical semigroup to display decoherence. The underlying notion of decoherence is that introduced by Blanchard and Olkiewicz (2003). We discuss this notion in some detail.