Editing Openai/6908ee36-d3b4-8010-a468-28e0753d08ae (section)

=== If the system is swept through an avoided crossing (control parameter λ(t)\lambda(t)λ(t) with rate λ˙\dot{\lambda}λ˙): ===

Pstay=exp⁡ ⁣(−πΔ22ℏ ∣ε˙∣),ε∝λ,P_{\text{stay}} = \exp\!\Big(-\frac{\pi \Delta^2}{2\hbar\,|\dot{\varepsilon}|}\Big),\quad \varepsilon\propto \lambda,Pstay=exp(−2ℏ∣ε˙∣πΔ2),ε∝λ,
and the effective transition window (latency) is set by the time interval where ∣ε∣≲Δ|\varepsilon|\lesssim \Delta∣ε∣≲Δ. If your states are driven by a slow HU background “clock,” this can give a natural τ\tauτ once Δ\DeltaΔ and ε˙\dot{\varepsilon}ε˙ are known.

==== 1. Pick your ontology for the hop: - Phase step on an internal rotation? → Use §4. Your current α\alphaα corresponds to N≈119N\approx 119N≈119. That makes the “factor of 10” vs. the rest-energy Heisenberg time unsurprising and physically harmless (it’s not an orthogonalization). - Literal tunneling between quasi-degenerate wells? → Use §2 + §3. Write a minimal 1D (or radial-4D) barrier, compute SSS, get Δ\DeltaΔ, then τ\tauτ. ====
# Cross-check with QSLs (§1): ensure your τ\tauτ respects MT/ML given the actual ΔE\Delta EΔE (level spread) of your coherence manifold, not mHc2m_Hc^2mHc2 unless the hop truly accesses that scale.
# If dissipation exists: include a dephasing time T2T_2T2 and relaxation T1T_1T1. The observable hop time is then τobs∼min⁡{πℏ/Δ, T2}\tau_{\text{obs}}\sim \min\{\pi\hbar/\Delta,\ T_2\}τobs∼min{πℏ/Δ, T2}.

==== - Compton period TC≈4.41×10−24 sT_C\approx 4.41\times 10^{-24}\,\text{s}TC≈4.41×10−24s. ====
* Your latency τ=αTC≈3.71×10−26 s\tau=\alpha T_C\approx 3.71\times10^{-26}\,\text{s}τ=αTC≈3.71×10−26s.
* If (and only if) we forced a full Rabi hop interpretation, it implies Δ∼πℏ/τ≈5.6×1010 eV\Delta\sim \pi\hbar/\tau\approx 5.6\times 10^{10}\,\text{eV}Δ∼πℏ/τ≈5.6×1010eV (tens of GeV) — clearly signaling that the Rabi-half-cycle picture is not the right one for your number.
* Interpreted as a phase step on an internal clock, it’s perfectly natural: N≈119N\approx 119N≈119 equal steps per TCT_CTC.

===== - Your “within a factor of 10” intuition against a naive Heisenberg rest-energy time is fine if the hop is a small phase advance on an internal rotation, not an orthogonalization. =====
* The best path to a principled estimate is to (a) decide whether the hop is a phase step or a true tunnel between wells, then (b) use either phase-step kinematics (§4) or WKB → splitting → Rabi (§§3–2), and finally (c) validate with QSL bounds (§1).

If you want, outline your preferred internal potential (even schematically: barrier height V0V_0V0, width LLL, effective mass meffm_\text{eff}meff), and I’ll compute τ\tauτ both via WKB (instanton) and via Wigner–Smith/dwell-time to see which regime lands closest to your α=0.00843\alpha=0.00843α=0.00843.