Localization Landscape in Non-Hermitian and Floquet quantum systems

Abstract

We propose a generalization of the Filoche--Mayboroda localization landscape that extends the theory well beyond the static, elliptic and Hermitian settings while preserving its geometric interpretability. Using the positive operator $H^\dagger H$, we obtain a landscape that predicts localization across non-Hermitian, Floquet, and topological systems without computing eigenstates. Singular-value collapse reveals spectral instabilities and skin effects, the Sambe formulation captures coherent destruction of tunneling, and topological zero modes emerge directly from the landscape. Applications to Hatano--Nelson chains, driven two-level systems, and driven Aubry--Andr\'e--Harper models confirm quantitative accuracy, establishing a unified predictor for localization in equilibrium and driven quantum matter.