Dynamically Regulated Spectral-Geometric Transport in Higher-Order Non-Hermitian Systems

This record contains the manuscript Dynamically Regulated Spectral-Geometric Transport in Higher-Order Non-Hermitian Systems by Francis Procaccia. The paper develops a unified theoretical framework for higher-order dispersive wave dynamics with dynamical stiffness regulation and non-Hermitian Floquet transport near exceptional points. It presents analytic results on stability, effective spectral geometry, Green functions, biorthogonal Berry curvature, adiabatic elimination, and geometric transport, along with numerical examples and a minimal computational implementation.

The work is intended as a research preprint and includes derivations, model definitions, numerical methodology, and representative results for reproducibility and scholarly discussion. Where applicable, the manuscript also clarifies the relationship between bulk geometric transport, coherence limits, and open-system effects, while distinguishing these results from speculative broader applications.

Keywords: non-Hermitian systems, exceptional points, Berry curvature, geometric transport, Floquet lattices, higher-order dispersion, dynamical regulation, open quantum systems, solitons, spectral geometry.