2005/07/15 by Jonathan Breuer, Peter J. Forrester, Breuer, Jonathan +3
Mathematics · #15A52 #81Q10 #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.math-ph/0507036
openalex publication_date 2005/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate random, discrete Schrödiner operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature β. They belong to the class of "critical" random Schrödiner operators with random potentials which diminish as |x|^-1/2. We show that as a function of β their eigenstates undergo a transition from extended (β≥ 2 ) to power-law localized (0 < β< 2).