- 94-392 Andries J., Fannes M., Tuyls P., Alicki R.
- The dynamical entropy of the quantum Arnold cat map
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Dec 8, 94
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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.
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