One-dimensional Discrete Anderson Model in a Decaying Random Potential: from a.c. Spectrum to Dynamical Localization

2020/01/21 by Olivier Bourget, Bourget, Olivier, Gregorio R. Moreno Flores +3
Engineering · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Terahertz technology and applications

paper · pdf · doi:10.48550/arxiv.2001.08131

openalex publication_date 2020/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a one-dimensional Anderson model where the potential decays in average like n^-α, α>0. This simple model is known to display a rich phase diagram with different kinds of spectrum arising as the decay rate α varies. We review an article of Kiselev, Last and Simon where the authors show a.c. spectrum in the super-critical case α>\frac12, a transition from singular continuous to pure point spectrum in the critical case α=\frac12, and dense pure point spectrum in the sub-critical case α

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