ANOSOV ACTIONS ON NONCOMMUTATIVE ALGEBRAS

An axiomatic framework for a quantum mechanical extension to the theory of Anosov systems is constructed, and it is shown that this retains some of the characteristic features of its classical counterpart, e.g., nonvanishing Lyapunov exponents, a vectorial K-property, and exponential clustering. The effects of quantization are investigated 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 quantization 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 on an Anosov system.