On localization for the Schrödinger operator with a Poisson random potential

2005/06/03 by Francois Germinet, François Germinet, Peter Hislop +5
Mathematics · Physics and Astronomy · #82B44 #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #msc:82B44

paper · pdf · doi:10.48550/arxiv.math-ph/0506012

openalex publication_date 2005/06/03 · arxiv created 2005/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove exponential localization for the Schrödinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson densities. In addition, we obtain dynamical localization and finite multiplicity of the eigenvalues.

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