2026/07/18 by Yi Cheng, Zongli Lin · 1 voice
#nlin.CD #physics.app-ph
Chirality in a discrete Zq spin interaction distinguishes clockwise from counterclockwise phase differences, but its manifestation in continuous nonlinear dynamics is unclear. We show that any pairwise Zq Hamiltonian admits a unique equilibrium-preserving embedding into a continuous phase-energy landscape that matches the discrete energy on the q-state phase grid, where every grid point is stationary. This embedding reveals that a Zq kernel is nonchiral if and only if the sine components of the relaxation vanish. Chirality of the discrete Zq model is therefore exactly the odd part of the continuous phase interaction. In the induced nonlinear phase dynamics, this odd part becomes an orientation-dependent phase shift in the multi-harmonic coupling, and chiral reversal flips this shift while preserving the coupling magnitudes. In self-sustaining oscillator networks, the shift is further realized as a direction-dependent delay. Transistor-level ring-oscillator simulations validate the predicted phase locking and reversal of directed phase bias. These results show that algebraic handedness in a discrete spin Hamiltonian can be represented as tunable time-domain asymmetry in continuous nonlinear dynamics.