Boundary preparation of strong Mpemba states in holography

Abstract

Finite boundary drives ending at the same charge density can select different relaxation channels. We demonstrate this in a probe Abelian--Higgs model on a fixed AdS black brane with a stable normal endpoint. Charge exchange during preparation modifies scalar propagation and source coupling. Density history and radial Maxwell feedback during and after the drive leave a cubic slow amplitude even after linear slow-mode cancellation. For the tested protocols at $ρ_f=3$, the density-history term interferes constructively with the net radial feedback; its modulus is 85--89\% of that of the total cubic coefficient. Calculated from the low-order equations alone, this total coefficient predicts the compensating pulse. Full nonlinear evolution confirms the reduction from $O(ε^3)$ to $O(ε^5)$ in the source amplitude $ε$, with approximately 600-fold suppression for the representative protocol at $ε=0.05$. Compensation extends the window of fast-channel relaxation without changing the final quasinormal-mode spectrum; early distance crossing already arises from linear interference. Fully tuned two- and three-pulse preparations suppress one and two slow modes, respectively, within numerical resolution. Local analysis establishes finite-pulse reachability of strong Mpemba states with vanishing selected asymptotic slow-mode coefficients. Charge-neutral controls retain a total-time advantage from a common input when the full subsequent control duration is included.