Ascertain whether the quench transient contains a subdominant secular resonance contribution

Ascertain whether the quench transient response near the resonance condition V=2|ε_b| contains a subdominant secular contribution that is masked by the background and finite observation-window effects.

Background

The paper tests a previously claimed narrow transient-amplitude resonance at V=2|ε_b|, which was attributed to a secular term in perturbation theory. Across the accessible damping rates and observation windows, the measured amplitude does not show the growth predicted when a simple single-mode secular contribution dominates.

The authors caution that the relevant response components are nearly collinear and that the measured scaling is window-dependent. Consequently, the data bound but do not exclude a smaller secular contribution superposed on the background, leaving its existence unresolved.

References

The calibrated conclusion is therefore a bound: over the tested lifetime range and observation windows, the measured response does not exhibit the growth expected when the simplest single-mode secular contribution dominates, while a smaller secular component superposed on the background is not excluded; the coarse ordering of that reference's Fig.~3 (larger amplitudes for V near $2|\varepsilon_b|$) is reproduced.

— Real-axis least-squares bath discretization for real-time transport in quantum-dot Josephson junctions  (2609.30000 - Zhou et al., 24 Sep 2026) in Section 3.3, subsection “Boundary: the transient resonance of Ref.~\cite{cheng2024quasiparticle}”