Spectral statistics of random Schrödinger operator with growing potential

Abstract

In this work we investigate the spectral statistics of random Schrödinger operators $H^{\omega }=-\Delta +{\sum }_{n\in {\mathbb{Z}}^d}(1+|n{|}^{\alpha })q_n(\omega )|{\delta }_n⟩⟨{\delta }_n|$, $\alpha >0$ acting on ${\ell }^2({\mathbb{Z}}^d)$ where $\{q_n{\}}_{n\in {\mathbb{Z}}^d}$ are i.i.d random variables distributed uniformly on $[0,1]$.

arXiv comment26 pages