Regensburg 2025 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 20: Many-body Quantum Dynamics II (joint session DY/TT)

DY 20.4: Vortrag

Mittwoch, 19. März 2025, 10:15–10:30, H37

Long-time Freeness in the Kicked Top — •Elisa Vallini and Silvia Pappalardi — University of Cologne, Köln, Germany

Recent work highlighted the importance of higher-order correlations in quantum dynamics for a deeper understanding of quantum chaos and thermalization. The full Eigenstate Thermalization Hypothesis, the framework encompassing correlations, can be formalized using the language of Free Probability theory. In this context, chaotic dynamics at long times are proposed to lead to free independence or "freeness" of observables. We investigate these issues in a paradigmatic semiclassical model - the kicked top - which exhibits a transition from integrability to chaos. Despite its simplicity, we identify several non-trivial features. By numerically studying 2n-point out-of-time-order correlators, we show that in the fully chaotic regime, long-time freeness is reached exponentially fast. These considerations lead us to introduce a large deviation theory for freeness that enables us to define and analyze the associated time scale. The numerical results confirm the existence of a hierarchy of different time scales, indicating a multifractal approach to freeness in this model. Our findings provide novel insights into the long-time behavior of chaotic dynamics and may have broader implications for the study of many-body quantum dynamics.

Keywords: Eigenstate Thermalization Hypothesis; Free probability; Long-time freeness; Higher-order correlations; Large deviation theory