Origin of the finite‑S scaling exponent in the low‑frequency crossover

Determine whether the observed finite‑spin scaling ω_S ∼ S^{-3/4}, which collapses the low‑frequency spectral function and fidelity susceptibility in the two‑spin chaotic model with couplings J=(3/2, π, √e) and A=x(√π, √3, e), arises from finite‑S corrections or indicates the presence of a distinct quantum time scale parametrically larger than the typical level spacing; characterize the mechanism and establish the correct asymptotic exponent.

Background

In the chaotic regime far from integrability, the authors find that finite‑S quantum data collapse onto classical behavior when frequencies are rescaled by ω_S ∼ S^{-3/4}, rather than by the naively expected Heisenberg scale ω_H ∼ 1/S. This unexpected exponent controls the low‑frequency cutoff of spectral functions and fidelities at finite S.

Clarifying whether this scaling reflects merely finite‑S corrections or a fundamentally new quantum time scale would inform how quantum effects persist near the classical limit and how they impact chaos diagnostics based on spectral functions.