Random discrete Schrödinger operators from random matrix theory

Abstract

We investigate random, discrete Schrödinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature β. They are similar to the class of 'critical' random Schrödinger operators with random potentials which diminish as . We show that as a function of β they undergo a transition from a regime of (power-law) localized eigenstates with a pure point spectrum for β < 2 to a regime of extended states with a singular continuous spectrum for β ⩾ 2.

Locations

• arXiv (Cornell University) - View - PDF
• Journal of Physics A Mathematical and Theoretical - View