Summary
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 III 1 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.
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Narnhofer, H. (2007). Quantum Anosov Systems. In: de Monvel, A.B., Buchholz, D., Iagolnitzer, D., Moschella, U. (eds) Rigorous Quantum Field Theory. Progress in Mathematics, vol 251. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7434-1_15
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