Spectral structure and controlled energy linearization of Feshbach effective Hamiltonians in a molecular quantum quench

Abstract: We establish spectral conditions under which a first-order energy linearization of a projected Feshbach Hamiltonian is controlled. When the support of the induced self-energy spectral measure lies entirely above or below the target energy window, the self-energy curvature and linearization remainder have fixed sign in the semidefinite (Löwner) order. The remainder then decreases monotonically under model-space enlargement by complete complementary-space spectral subspaces, and the minimax linearization energy is determined by the endpoint norms. Far-separated asymptotics and the near-boundary divergence caused by an approaching pole are obtained explicitly. The theory is validated by a numerically exact sudden-quench calculation for the two-electron system $HT$ -> $^3HeH^+$: all 56 nontrivially coupled basis-geometry cases have support separated above the target window, while seven cc-pVTZ cases are exactly decoupled by construction and serve as numerical control cases. The same remainder controls the projected resolvent and, through source dressing, the full prepared-state response, with resolvent amplification governing the near-pole sensitivity. These results provide a practical criterion for controlled downfolding in molecular electronic structure and for final-state analyses in neutrino-mass experiments.

This is a major revision that replaces the original manuscript. While v1 developed a numerical transport scheme for sudden-approximation overlaps in nuclear β-decay, the present work establishes a new spectral criterion for controlled local approximation of Feshbach effective Hamiltonians

Chemical Physics (physics.chem-ph); Quantum Physics (quant-ph)

arXiv:2604.23910 [physics.chem-ph]

(or arXiv:2604.23910v2 [physics.chem-ph] for this version)