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This research establishes a direct link between the spatial morphology of scarred eigenstates and operator scrambling dynamics in chaotic quantum billiards. By demonstrating that specific geometric recurrences act as templates for OTOC growth rather than just static violations of ergodicity, the study provides new diagnostic tools for understanding weak ergodicity breaking. The work advances fundamental theory on how structural memory influences information spreading in isolated quantum systems without immediate practical application to current hardware or algorithms.
Morphology-resolved scrambling in a chaotic quantum billiard
arXiv:2606.16865v1 Announce Type: new Abstract: Chaotic quantum systems can retain spatial memory through scarred eigenstates, but whether these static structures control scrambling remains unclear. This work establishes a morphology-resolved connection between scarred eigenstates and eigenstate-resolved OTOCs in a peanut-shaped quantum billiard. Scalar localisation diagnostics, including differential entropy and continuum participation ratios, detect anomalous concentration but discard spatial architecture. A scale-normalised density overlap, in contrast, directly compares probability density profiles, revealing families of orthogonal eigenstates with nearly identical spatial morphology. Comparing the complete OTOC time traces of these orthogonal eigenstates reveals that morphological recurrence has dynamical content: moderate density overlap yields no universal prediction, whereas strongly recurring morphologies exhibit nearly identical OTOC growth and saturation. Thus, scarred structures act as spatial templates for operator growth, not merely static violations of ergodicity. This morphology-resolved framework turns eigenstate shape into a quantitative predictor of scrambling and provides a scale-controlled diagnostic of weak ergodicity breaking in quantum chaos.
Abstract:Chaotic quantum systems can retain spatial memory through scarred eigenstates, but whether these static structures control scrambling remains unclear. This work establishes a morphology-resolved connection between scarred eigenstates and eigenstate-resolved OTOCs in a peanut-shaped quantum billiard. Scalar localisation diagnostics, including differential entropy and continuum participation ratios, detect anomalous concentration but discard spatial architecture. A scale-normalised density overlap, in contrast, directly compares probability density profiles, revealing families of orthogonal eigenstates with nearly identical spatial morphology. Comparing the complete OTOC time traces of these orthogonal eigenstates reveals that morphological recurrence has dynamical content: moderate density overlap yields no universal prediction, whereas strongly recurring morphologies exhibit nearly identical OTOC growth and saturation. Thus, scarred structures act as spatial templates for operator growth, not merely static violations of ergodicity. This morphology-resolved framework turns eigenstate shape into a quantitative predictor of scrambling and provides a scale-controlled diagnostic of weak ergodicity breaking in quantum chaos.
Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); High Energy Physics - Theory (hep-th); Chaotic Dynamics (nlin.CD); Computational Physics (physics.comp-ph)
arXiv:2606.16865 [quant-ph]
(or arXiv:2606.16865v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.16865 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 183 words
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