94-138 G.G. Emch, H. Narnhofer, G.L. Sewell, W. Thirring

Anosov Actions on Non--Commutative Algebras (60K, LaTeX) May 26, 94

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Abstract. We construct an axiomatic framework for a quantum mechanical extension to the theory of Anosov systems, and show that this retains some of the characteristic features of its classical counterpart, e.g. positive Lyapunov exponents, a vectorial K--property, and exponential clustering. We then investigate the effects of quantisation on two prototype examples of Anosov systems, namely the iterations of an automorphism of the torus (the `Arnold Cat' model) and the free dynamics of a particle on a surface of negative curvature. It emerges that the Anosov property survives quantisation in the case of the former model, but not of the latter one. Finally, we show that the modular dynamics of a relativistic quantum field on the Rindler wedge of Minkowski space is that of an Anosov system.

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