Deletion Does Not Measure Contribution in Coupled-Channel Dynamics

Abstract: In projected descriptions of quantum dynamics, the importance of an eliminated degree of freedom is routinely assessed by deleting it and measuring the system's response. This conflates two effects: the channel's intrinsic contribution and the reorganization of the surviving model space. Here we disentangle them in continuum-discretized coupled-channels (CDCC) scattering, decomposing the Feshbach dynamic polarization potential (DPP) channel by channel while keeping the full Green's function intact, and comparing with conventional bin-deletion from the coupled equations. For $d$+$^{58}$Ni the two approaches reproduce the same elastic $S$-matrix to 0.45\%, yet a channel ranked first by one diagnostic is ranked fifth by the other. A frozen-basis protocol, zeroing couplings without reducing the basis, yields rankings that track the DPP closely ($ρ{\rm DPP,frozen} = 0.94$) and are uncorrelated with standard deletion ($ρ{\rm frozen,del} = -0.37$), establishing that the discrepancy is dominated by model-space reorganization. Pairwise analysis reveals quantum anti-synergy: adjacent channels partially cancel through off-diagonal Green's-function coherence, in all 10 tested pairs by the DPP and 8 of 10 by deletion. The asymmetry between excluding a degree of freedom from the effective interaction and deleting it from the model space is algebraic and general; basis-preserving decoupling, implementable in any coupled-channel code, isolates the reorganization component.