Universal Spectral Correlation between Hamiltonians with Disorder

TL;DR

This paper derives a universal spectral correlation function for pairs of disordered Hamiltonians, revealing a broad applicability across various random distributions in quantum systems.

Contribution

It provides an explicit calculation of the spectral correlation function showing its universal form for a wide class of disordered Hamiltonians.

Findings

Spectral correlation function has a universal form.

Applicable to broad class of random distributions.

Enhances understanding of spectral properties in disordered quantum systems.

Abstract

We study the correlation between the energy spectra of two disordered Hamiltonians of the form $H_a=H_{0a}+s_{a}\varphi$ ($a=1,2$) with $H_{0a}$ and $\varphi$ drawn from random distributions. We calculate this correlation function explicitly and show that it has a simple universal form for a broad class of random distributions.