Quantum site percolation on amenable graphs

TL;DR

This paper studies quantum site percolation on graphs with amenable group actions, establishing fundamental spectral properties such as non-random spectra, self-averaging density of states, and trace formulas.

Contribution

It introduces a quantum percolation model on amenable graphs and proves key spectral properties that were previously unknown in this setting.

Findings

Spectrum is non-random across realizations

Existence of a self-averaging integrated density of states

Derivation of a trace-formula for the model

Abstract

We consider the quantum site percolation model on graphs with an amenable group action. It consists of a random family of Hamiltonians. Basic spectral properties of these operators are derived: non-randomness of the spectrum and its components, existence of an self-averaging integrated density of states and an associated trace-formula.