Quantization of Classical Maps with tunable Ruelle-Pollicott Resonances

Abstract

We investigate the correspondence between the decay of correlation in classical system, governed by Ruelle--Pollicott resonances, and the properties of the corresponding quantum system. For this purpose we construct classical systems with controllable resonances together with their quantum counterpart. As an application of such tailormade resonances we reveal the role of Ruelle--Pollicott resonances for the localization properties of quantum energy eigenstates.

REVTeX4 (using graphics and pstricks packages), 18 pages, 16 figures

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• Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory
• Spectral Statistics Beyond Random Matrix Theory
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• Frobenius-Perron Resonances for Maps with a Mixed Phase Space
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Cited by in corpus (4)

• Out-of-time-ordered correlator in the quantum bakers map and truncated unitary matrices
• Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
• Semiclassical Formulae For Wigner Distributions
• Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard