Mapping Proton Transport to 1D Domain-Wall Dynamics: Metrics \(B, L, 2f\) and Thresholds

This work presents “Mapping Proton Transport to 1D Domain-Wall Dynamics: Metrics B, L, 2f and Thresholds,” an operational framework that recasts proton motion in wires and lane devices into a one-dimensional dual mapping. Eigen (site-centered) states and Zundel (bond-centered) states are treated as ordered regions and domain walls, respectively. A small-bond MPO/MPS workflow—motivated by recent dual-optimization ideas in tensor networks (Lootens–Delcamp–Verstraete, Nature Physics 2025, doi:10.1038/s41567-025-02961-2)—places each lane in a low-entanglement dual sector, cutting parameters and speeding fits. Two prior pieces anchor the physics and the device design: (1) “Six-Water Proton Wire: From Symmetry to Asymmetry via Double Tilt, and Falsifiable Tests” (Zenodo, doi:10.5281/zenodo.17117888), which defines the double-tilt control and the B, L, 2f metrics with falsifiers (flip-only Z, disable-L, isotope swap), and (2) “Midplane H+ Proton Lanes: Geometry, Double Tilt, and Drift,” which implements a 2D-to-many-1D reduction via Debye focusing (lambda_D ~ h/2) and a small transverse bias across a 1–2 nm gap. The mapping clarifies why a modest 10–30 mV transverse bias can suppress side/back hops, enforce monotone drift, and push the dual ground state into a symmetry-broken, near-product form. What is new here is the end-to-end bridge: a physical dual dictionary for proton transport (Eigen on sites, Zundel on bonds), a lane device that realizes many weakly coupled 1D chains in parallel, a bench run card for fast validation (build → bias → odd/even checks → threshold sweep), and a compact MPO/MPS inference loop for B, L, 2f and onset thresholds. The result is a falsifiable, scalable program: optimize in dual, verify in real space, and map back for interpretation, with clear pass/fail signatures (odd/even demodulation, disable-L collapse, H↔D shifts) and linear scaling across lanes until transverse coupling turns on.