Spin-Momentum Impedance and Filtering by a Spin-Coupled Absorbing Boundary Condition

arXiv:2606.25650v1 Announce Type: new Abstract: Absorbing boundaries are often treated as scalar sinks. Here we show that a spin-coupled absorbing boundary for a Pauli particle acts instead as a spin–momentum impedance. Its tangential boundary symbol has two branches, $i\kappa\pm|\boldsymbol{\xi}|$, coupling normal absorption to in-plane momentum. In a harmonic guide, the transverse ground state samples $|\boldsymbol{\xi}|\sim \ell_\perp^{-1}\sim\sqrt{\omega}$; narrowing the guide therefore strengthens a local evanescent boundary response without introducing a bulk potential barrier. Solving the detector-present spinor absorbing-boundary evolution, we identify boundary-induced filtering: the prompt detector flux is suppressed, the fixed-window detected fraction is reduced, and a delayed oscillatory sector appears. Over that window the restricted mean detection time is fitted by $A+B\sqrt{\omega}$, with setup-dependent coefficients. The robust result is a spin–momentum filtering mechanism with boundary scale $|\boldsymbol{\xi}|\sim\sqrt{\omega}$, not a universal arrival-time law.