Transition Dynamics of Localized Excitations in a Finite-Response Medium

We present a finite-response medium model for localized excitations within the Emergent Condensate Superfluid Medium (ECSM) framework. Bound radial–angular modes arise naturally from an effective response potential, producing a discrete spectrum with well-defined degeneracy structure. Transition amplitudes between modes are computed using overlap integrals of the underlying response fields. We show that selection rules are not imposed externally, but emerge from the symmetry of the response perturbation. For dipole-like perturbations, the dominant transitions satisfy Δℓ = ±1 and Δm = 0. Transition strengths are further modulated by the coherence parameter χ, which suppresses coupling in the finite-response regime. These results demonstrate that key structural features typically associated with quantum selection rules can arise directly from the physics of a finite-response medium.