Quantum Anosov Systems
The concept of Anosov flows and of Kolmogorov systems can be translated from classical to quantum systems. It is shown that modifications of the concepts are necessary to keep the same clustering behavior as is typical for classical Anosov systems. With such modifications, Anosov structure appears rather naturally in a type III1 algebra. Here Anosov structure and Kolmogorov structure with respect to modular evolution are even equivalent. The Rindler wedge of quantum field theory offers a typical example.
KeywordsLyapunov Exponent Automorphism Group Invariant State Cluster Property Modular Evolution
Unable to display preview. Download preview PDF.
- 1.H. Araki and L. Zsido: Extension of the structure theorem of Borchers and its application to half-sided modular inclusions. arXiv:math.OA/0412061.Google Scholar
- 6.H.-J. Borchers: On the revolutionization of quantum field theory by Tomita’s modular theory. Preprint ESI, 1999.Google Scholar