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.