Hybrid dynamics of diffusing Majorana defects: amplitudes, parity regimes, and braiding-induced connectivity

Replacing classical domain walls in Ising chains with Majorana defects can raise nonlocal topological cooling Hilbert space that stores parity information. We simulate diffusion–annihilation dynamics starting from high-defect, dimerized initial states and show that, although the late-time decay remains in the A+A→∅ universality class with ρ(t)∝1/√(8πDt), the governing amplitude is topology-dependent. If any bonds start in odd parity, the asymptotic amplitude is exactly 2; for all-even initial parity, the amplitude becomes 2y(2−y), where y is the intrapair-length fraction, revealing a mean-field constraint from parity variance analogous to magnetization in the Ising voter model. Mapping to two coupled classical chains clarifies the role of expected bond parity \bar n and identifies the parity operator's variance as the quantum Fisher information that controls decay amplitudes and correlators. Extending to N stacked chains with probabilistic interlayer braiding—unitary exchanges that reshuffle pairing—we find braiding restores the symmetry broken in the all-even sector while lowers the total-defect density to ρ(t)=(N+1)/√(8πDt), independent of local braiding range, set by the number of independent exchange classes. Our results expose a hybrid quantum–classical in which topologically protected information back-reacts on classical defect motion and sets universal amplitudes.