Non-Normal Amplification in Extreme Regimes: Operator Growth in High-Energy and Strong-Field Systems

Abstract We investigate transient amplification mechanisms in systems operating under extreme conditions, including high-energy and strong-field regimes. While classical stability analysis focuses on spectral properties of governing operators, we demonstrate that non-normality leads to significant amplification effects even when spectral criteria indicate stability. Using operator-theoretic methods and pseudospectral analysis, we establish bounds on transient growth in systems characterized by strong coupling and high interaction density. We extend the K-functional framework to extreme regimes and identify structural conditions under which amplification dominates system dynamics.