Intermediate-time growth law of length-basis negativity

Determine whether the Wigner negativity of the Hartle–Hawking state in the JT-gravity length basis follows the same slow power-law growth between the disk era and the Heisenberg time as the negativity in the discrete GUE Krylov basis, thereby resolving the intermediate regime left undetermined by the disk analysis.

Background

The paper determines the disk-era negativity of the Hartle–Hawking state and argues that it remains approximately constant, while the late-time quantum plateau is inferred from spectral discreteness and an effective-Haar assumption. The transition between these regimes is not obtained by the disk-level calculation.

The authors compare this unresolved intermediate behavior with the discrete GUE model in the Krylov basis, where the negativity reportedly grows as a power law before saturating at exponentially long times. Establishing whether an analogous law holds in the JT-gravity length basis would determine the missing time dependence between the semiclassical disk era and the Heisenberg-time regime.

References

In the discrete GUE model in the Krylov basis, the analogous growth is a slow power law at $O(1)$ times followed by saturation at exponential times; whether the length-basis negativity of the HH state follows the same law between the disk era and $t_{\rm H}$ is the main open quantitative question left by this paper.

— Complexity study of the Hartle-Hawking state in JT gravity  (2610.00844 - Basu, 1 Oct 2026) in Section 4.4, subsection “The quantum plateau: discreteness fixes the saturation value” (also reiterated in Section 6, subsection “Order-parameter normalisation,” and Section 8, paragraph “Probes and clocks”)