Unifying short‑ and long‑time chaos probes

Develop a unified theoretical framework that connects short‑time chaos diagnostics (such as out‑of‑time‑order correlators and operator spreading in Krylov space) with long‑time sensitivity measures based on adiabatic transformations, spectral low‑frequency behavior, and fidelity susceptibility.

Background

The authors argue that short‑time probes (OTOCs, operator growth) and long‑time probes (fidelity susceptibility via low‑frequency spectral weight) capture different aspects of dynamics and can yield conflicting indications near the classical limit. In their examples, high‑frequency decay of spectral functions does not distinguish integrable from chaotic dynamics, whereas low‑frequency behavior does.

A principled connection between these regimes would clarify how early‑time scrambling relates to late‑time instability of observables and could reconcile different operational definitions of chaos across quantum and classical domains.

References

The question of how to connect these short- and long- time probes of dynamics remains an interesting and unsolved problem.

— Defining classical and quantum chaos through adiabatic transformations  (2401.01927 - Lim et al., 2024) in Section 7 (Conclusions)

While spectral statistics and OTOCs serve as central diagnostics of quantum chaos, the precise connection between these early-time and late-time diagnostics remains a major open question, lying at the intersection of chaos, thermalization, and the fundamental limits of quantum dynamics.

— Quantum Chaos and Spread of States in Krylov Subspace: A Topical Review  (2608.26825 - Jeong et al., 27 Aug 2026) in Section 1, Introduction

The relation between the present classical result and these quantum constructions remains to be clarified.

— Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation  (2609.11340 - Matsumoto et al., 10 Sep 2026) in Concluding remarks