Defect-Induced Non-Abelian Mixing and Dissipative Reduction

We propose a dynamical framework based on three discrete Möbius-type phase loops, modelled as a three-channel state in ℂ³. As the inter-layer separation collapses, a blow-up tendency develops, leading to energy concentration near a central defect. At this stage, inter-layer interactions activate a non-commuting su(3)-like mixing structure, whose time-ordered accumulation is captured by a Dyson expansion. Interpreting the evolution as a path in parameter space yields a Wilczek–Zee connection, with curvature F = dA + A ∧ A encoding defect-centred path dependence. This curvature reflects the non-abelian nature of the inter-layer dynamics and governs the redistribution of phase error across the system. A curvature-correlated dissipation mechanism selectively suppresses high-curvature modes, inducing an effective reduction of the active mixing sector from su(3) to su(2), and ultimately to an abelian u(1) regime. The terminal state corresponds to a stable, irreducible configuration associated with the defect. Although the model is formulated independently of specific partial differential equations, its structure exhibits a strong analogy with dissipative concentration–redistribution mechanisms in nonlinear systems, suggesting potential connections with fluid and gauge dynamics.