The Egorov property in perturbed cat maps

DOI10.1088/1751-8113/40/32/004zbMATH Open1120.81055arXiv0706.4397OpenAlexW3102881157WikidataQ62591286 ScholiaQ62591286MaRDI QIDQ5757630

Martin Horvat, Mirko Degli Esposti

Publication date: 7 September 2007

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

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 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.

Full work available at URL: https://arxiv.org/abs/0706.4397

Mathematics Subject Classification ID

Quantum chaos (81Q50) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fractals (28A80)

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