Forecast long‑time OTOC behavior from finite‑time observations

Determine whether a general, model‑independent procedure exists to extrapolate from finite‑time observations of out‑of‑time‑ordered correlators of few‑body observables to rigorous long‑time (or infinite‑time) predictions of pure‑state thermalization in autonomous unitary (Hamiltonian) many‑body dynamics; either construct such a procedure or prove that no such general procedure exists.

Background

The paper develops a method to establish pure‑state quantum thermalization without statistical averages using out‑of‑time‑ordered correlators (OTOCs). Unlike earlier autocorrelator‑based results that allow extrapolation from finite‑time observations to long‑time conclusions for second‑order correlators, the present OTOC‑based framework yields constraints only at the observed times.

The authors explain that their prior autocorrelator results provide long‑time forecasts from short‑time data in autonomous dynamics, but a corresponding accessible, system‑independent extrapolation for OTOCs is missing. They explicitly note that it is not clear whether such forecasts are possible in general and suggest identifying a method (or proving impossibility) as an outstanding issue. This challenge is also connected to Appendix A.3, which argues that straightforward extensions of earlier techniques do not yield useful long‑time bounds for fourth‑order correlators.