Sharp Locking Costs in Paired Skyrme Fields

Sharp Locking Costs in Paired Skyrme Fields investigates the energy required to force two coupled SU(2) fields with different topological winding numbers into near agreement. For fields carrying individual quadratic and quartic Skyrme energies, the paper establishes matching lower and upper bounds showing that the energy infimum in each fixed unequal-winding sector grows as Θ(λ^{1/6}) as the potential-locking strength λ increases. The proof combines an explicit inequality relating topological mismatch to field separation and energy with a smooth, quantitative rank-one approximation that achieves the same scaling. This exponent persists with fixed derivative locking, bounded nonnegative host potentials, and electrostatic self-energy. Further results constrain relative-current concentration, identify exact energy infima in equal-winding sectors, and provide sufficient conditions for neutral-sector binding against every finite topological partition. These findings characterize the energetic consequences of topological mismatch while leaving the existence and dynamical stability of charged minimizers open.