Frequency-Window Operation Semantics of a Parametrically Driven Discrete Sine-Gordon Kink

Abstract

In a discretely breathing sine-Gordon chain, the fate of a moving kink is organized by three characteristic frequencies into frequency-separated operation windows: a mobility transport band (approx. 1.2-1.6 f0, persistent directed transport), a shape-mode resonance band (f approx. f_b; 1:1 forced resonance to kink-pair production and complete annihilation = field-driven erasure), and the primary parametric-resonance region (2f_b/sqrt(1+eps/2) and above; background heating chaos). The Mathieu threshold closes at three points (deviations <=0.01); the shape-mode forcing amplitude is given in closed form F0=2*eps*omega0^2; pair production exhibits an amplitude threshold eps_c in (0.20, 0.25]. All numerics pre-registered (16 rounds); kink localization uses the drift-immune gold-standard observable argmax(1-cos(theta)); includes a methodological result on the four-generation failure analysis of velocity observables. A minimal model of a frequency-programmable write/erase medium.