Andries J., Fannes M., Tuyls P., Alicki R.
The dynamical entropy of the quantum Arnold cat map
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ABSTRACT.  We present a rigorous computation of the dynamical entropy $h$ of the 
quantum Arnold cat map. This map, which describes a flow on the 
non-commutative two-dimensional torus, is a simple example of a quantum 
dynamical system with optimal mixing properties, characterized by Lyapunov 
exponents $\pm \ln \lambda^+$, $\lambda^+>1$. We show that, for all values 
of the quantum deformation parameter, $h$ coincides with the positive 
Lyapunov exponent of the dynamics.