Non-stationary Anderson Localization

2024/03/24 by Anton Gorodetski, Victor Kleptsyn, Gorodetski, Anton +1 · 2 citations
Mathematics · #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2403.15970

Abstract

We consider discrete Schrödinger operators on ℓ²(ℤ) with bounded random but not necessarily identically distributed values of the potential. We prove spectral localization (with exponentially decaying eigenfunctions) as well as dynamical localization for this model. An important ingredient of the proof is a non-stationary version of the parametric Furstenberg Theorem on random matrix products, which is also of independent interest.

Cited by

• Localization of the 1D Non-Stationary Anderson Model
• The fibered rotation number

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