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

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, $i\kappa \pm |\mathbf{\xi }|$, coupling normal absorption to in-plane momentum. In a harmonic guide, the transverse ground state samples $|\mathbf{\xi }|\sim {\ell }_{\perp }^{-1}\sim \sqrt{\omega }$; 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 $|\mathbf{\xi }|\sim \sqrt{\omega }$, not a universal arrival-time law.

10 pages, 1 figure; includes 29-page Supplementary Information with 5 supplementary figures