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Participation ratio as a quantum probe of hierarchical stickiness
Ariel A Galindo Duque1, Miguel A Prado Reynoso1,2, Miguel Gonzalez1,3
1Instituto de Ciencias Nucleares, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 Cd. Mx., Mexico.
Abstract:
We investigate how quantum localization encodes the hierarchical stickiness that governs transport in mixed classical phase spaces. Using the periodically driven kicked top, we show that the participation ratio of coherent states in the Floquet eigenbasis quantitatively reflects the hierarchical organization of sticky regions identified classically through finite-time Lyapunov exponent (FTLE) statistics. To establish a quantitative quantum-classical correspondence, we introduce a Gaussian coarse graining of the FTLE matched to the intrinsic semiclassical resolution of coherent states. Both local correlations and global comparisons of probability distributions demonstrate that quantum and classical indicators agree optimally within a finite window of evolution times, where sticky structures are most clearly resolved. Our results promote the participation ratio from a global measure of chaos to a sensitive probe of hierarchical transport and provide a practical framework for diagnosing anomalous localization in driven quantum systems.
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