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This study establishes a quantitative link between quantum participation ratios and classical finite-time Lyapunov exponents, demonstrating that quantum localization effectively encodes hierarchical transport structures in mixed phase spaces. By introducing Gaussian coarse graining to match semiclassical resolution, the authors provide a practical diagnostic tool for identifying anomalous localization and sticky dynamics in driven quantum systems. The work advances the understanding of chaos quantification by elevating the participation ratio from a global metric to a sensitive probe of layered transport mechanisms.
Participation Ratio as a Quantum Probe of Hierarchical Stickiness
arXiv:2602.18412v2 Announce Type: replace 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 (PR) of coherent states in the Floquet eigenbasis resolves the same layered structure that appears classically as a multimodal distribution of finite-time Lyapunov exponents (FTLEs). To establish a quantitative 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 route for diagnosing anomalous localization in driven quantum systems.
Authors:Ariel A. Galindo Duque (1), Miguel A. Prado Reynoso (1 and 2), Miguel Gonzalez (1 and 3), Jorge G. Hirsch (1) ((1) Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México. (2) Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, España. (3) Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Republic of Korea.)
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 (PR) of coherent states in the Floquet eigenbasis resolves the same layered structure that appears classically as a multimodal distribution of finite-time Lyapunov exponents (FTLEs). To establish a quantitative 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 route for diagnosing anomalous localization in driven quantum systems.
Quantum Physics (quant-ph); Chaotic Dynamics (nlin.CD)
arXiv:2602.18412 [quant-ph]
(or arXiv:2602.18412v2 [quant-ph] for this version)
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