Spectra of Anderson type models with decaying randomness

1999/11/08 by M. Krishna, Krishna, M., Kalyan B. Sinha +2
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.math-ph/9911009

arxiv created 1999/11/08 · openalex publication_date 1999/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider some Anderson type models, with decaying randomness and the free parts having long range tails. The randomness may decay at different rates in different directions, though in majority of directions we require some sort of short range decay. We show that there is pure a.c. spectrum and some pure point spectrum in such models.

Citations

• Localization and mobility edge for sparsely random potentials
• Singular continuous spectrum under rank one perturbations and localization for random hamiltonians

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