Universal Spectral Correlation between Hamiltonians with Disorder

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.