Bogoliubov mode dynamics and non-adiabatic transitions in time-varying condensed media

Abstract

This study investigates non-adiabatic wave dynamics in condensed media and the transition from adiabatic stability to spectral chaos. We introduce a dimensionless parameter, as a universal metric to quantify phase-mode redistribution at sub-wavelength inhomogeneities. Our framework treats defects as localized sites of adiabaticity violation triggering non-adiabatic parametric excitation of the ground state. Numerical validation in an expanded 50-level bosonic basis demonstrates that the framework accurately distinguishes between adiabatic regimes in ENZ-metamaterials and non-adiabatic transitions in ultrafast magnetic media. We establish a universal scaling law governed by the non-adiabaticity-to-regulation ratio, proving that the proposed metric remains a robust metrological tool for identifying sub-wavelength inhomogeneities across diverse material classes. Computational singularities observed at extreme loads identify the rigorous operational boundaries for coherent mode-mixing. The robustness of the proposed framework is numerically validated, proving the method's reliability for a wide class of non-linear condensed media satisfying the stability criterion. This result provides a rigorous physical justification for the dynamic Hilbert space truncation (effective fermion-like dynamics), ensuring metrological consistency in complex structural environments. These results provide a theoretical foundation for probing ultrafast collective excitations and latent internal stresses, extending structural analysis beyond the traditional diffraction barrier.