Delocalization for the 3D discrete random Schrödinger operator at weak disorder (Q2876344)

The authors study the 3D random discrete Schrödinger operators, given by \(H_\omega=-\Delta+\sum_{i\in Z^3} \omega_i<\cdot,\delta_i>\delta_i\) on \(l^2(\mathbb Z^3),\) where the random variables \(\omega_i\) are i.i.d. with uniform distribution in \([-c/2,c/2]\). The authors apply a recently developed approach [\textit{C. Liaw}, J. Stat. Phys. 153, No. 6, 1022--1038 (2013; Zbl 1302.82011)] to study the existence of extended states at small disorder and show that for disorder \(c\lesssim 2.0,\) numerical experiments indicate that this operator does not exhibit Anderson localization with positive probability, in the sense that it has non-zero absolutely continuous spectrum with probability 1.