Dynamical Chaos and Many-Body Quantum Systems

Eduardo Jonathan Torres-Herrera, Léa Ferreira dos Santos

Isaías Vallejo-Fabila, Adway Kumar Das, Sayan Choudhury +1 more

We demonstrate that the dynamics of an observable localized at a single-site is sufficient to determine whether a many-body quantum system exhibits level statistics characteristic of random matrix theory, which is a widely used diagnostic of quantum chaos. Specifically, we analyze the spin autocorrelation function at a single site evolving under a disordered spin-1/2 chain, a setup realizable in ongoing experimental platforms. We also investigate the partial (subsystem) survival probability, recently measured in cold-atom experiments, thereby broadening discussions on detecting many-body quantum chaos via survival probability [Phys. Rev. Res. 7, 013181 (2025)2643-156410.1103/PhysRevResearch.7.013181]. Given the precision and timescales currently achievable, our results indicate that the detection of many-body quantum chaos through dynamical observables is feasible but constrained to small system sizes.

Gary E. Mitchell

A. G. Lazerson, Alexey Alexeevich Boikov

Kaito Kobayashi, Yukitoshi Motome

Reservoir computing (RC) is a machine learning paradigm that harnesses dynamical systems as computational resources. In its quantum extension-quantum reservoir computing (QRC)-these principles are applied to quantum systems, whose rich dynamics broadens the landscape of information processing. In classical RC, optimal performance is typically achieved at the "edge of chaos," the boundary between order and chaos. Here, we identify its quantum many-body counterpart using the QRC implemented on the celebrated Sachdev-Ye-Kitaev model. Our analysis reveals substantial performance enhancements near two distinct characteristic "edges": a temporal boundary defined by the Thouless time, beyond which system dynamics is described by random matrix theory, and a parametric boundary governing the transition from integrable to chaotic regimes. These findings establish the "edge of many-body quantum chaos" as a design guideline for QRC.

Peter O’Donovan, Neil Dowling, Kavan Kishore Modi +1 more

The process tensor provides a general representation of a quantum system evolving under repeated interventions and is fundamental for numerical simulations of local many-body dynamics. In this work, we introduce the projected process ensemble, an ensemble of pure output states of a process tensor in a given basis of local interventions, and use it to define increasingly more fine-grained probes of quantum chaos. The first moment of this ensemble encapsulates numerous previously studied chaos quantifiers, including the Alicki-Fannes quantum dynamical entropy, butterfly flutter fidelity, and spatiotemporal entanglement. We discover characteristic entanglement structures within the ensemble’s higher moments that can sharply distinguish chaotic from integrable dynamics, overcoming deficiencies of the quantum dynamical and spatiotemporal entropies. These conclusions are supported by extensive numerical simulations of many-body dynamics for a range of spin-chain models, including noninteracting, interacting-integrable, chaotic, and many-body localized regimes. Our work elucidates the fingerprints of chaos on spatiotemporal correlations in quantum stochastic processes and provides a unified framework for analyzing the complexity of unitary and monitored many-body dynamics.