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engines/quan_loncar_v1/package/quan_loncar_optimizer/engine/quan_loncar_series_phase23/README.md · assembled 2026-07-29 15:57 UTC.

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Quan--Loncar series, Phase 23

Phase 23 replaces the abandoned Cartesian tensor-product evaluation of the compact transverse Maxwell term with shell-subtracted polar quadrature.

The radial pole at q^2 = k_c^2-beta^2 is removed from the numerical integrand, and its logarithmic contribution is added analytically on the outgoing sheet. Complex shell Fourier factors use Phi(-q) on the left; complex conjugation would destroy analyticity and invalidate implicit or automatic differentiation.

The radial nodes are fixed in q*T/2 and the angular nodes are a fixed periodic trapezoidal rule. Consequently geometry changes affect smooth integrands and explicit scale factors, not discrete node topology.