Egorov property in perturbed cat map

Abstract. We study the time evolution of the quantum-classical correspondence (QCC) for the well known model of quantised perturbed cat maps on the torus in the very specific regime of semi-classically small perturbations. The quality of the QCC is measured by the overlap of classical phase-space density and corresponding Wigner function of the quantum system called quantum-classical fidelity (QCF). In the analysed regime the QCF strongly deviates from the known general behaviour discussed in [1], in particular it decays faster then exponential. Here we study and explain the observed behavior of the QCF and the apparent violation of the QCC principle.