Level Spacing for Non-Monotone Anderson Models

TL;DR

This paper establishes localization and probabilistic bounds on the minimum energy level spacing in a non-monotone Anderson model, providing detailed insights into the spectral structure and eigenfunction decay.

Contribution

It introduces a novel approach using energy windows and Schur complements to analyze level spacing without monotonicity assumptions.

Findings

Proves localization in non-monotone Anderson models.

Provides probabilistic bounds on minimum level spacing.

Details microscopic spectral structure and eigenfunction decay.

Abstract

We prove localization and probabilistic bounds on the minimum level spacing for a random block Anderson model without monotonicity. Using a sequence of narrowing energy windows and associated Schur complements, we obtain detailed probabilistic information about the microscopic structure of energy levels of the Hamiltonian, as well as the support and decay of eigenfunctions.