Negative Dwell Times as Resolvent Derivatives: A Structural Operator-Theoretic Explanation of 𝑻𝑻=𝒕𝒈

This dataset and manuscript present a structural operator‑theoretic explanation of negative group delays and post‑selected excitation times in resonant atomic media. The work demonstrates that the equality TT=tg arises naturally from the shared analytic structure of the internal resolvent R(ω)=(ω0−ω−iΓ/2)−1, which governs susceptibility, transmission amplitude, and excited‑state dynamics. A self‑contained conditional‑probability derivation (§5.7) establishes TT=Im[∂ωln⁡t(ω)]ω0 directly from the resolvent, closing the logical gap between quantum‑trajectory and structural proofs. Negative values of both quantities near resonance are shown to result from spectral reshaping, not superluminal propagation.