Correlation of local densities of states on mesoscopic energy scales in random band matrices

TL;DR

This paper investigates the correlation behavior of local densities of states in two-dimensional random band matrices, revealing oscillatory correlations in the diffusive regime related to system size and bandwidth.

Contribution

It provides new insights into the phase transition of correlation functions of local densities of states in 2D random band matrices at mesoscopic scales.

Findings

Local densities of states exhibit alternating positive and negative correlations.

Correlations oscillate approximately O(log(L/W)) times in the diffusive regime.

Results enhance understanding of spectral correlations in mesoscopic disordered systems.

Abstract

We are interested in the phase transition of the correlation function of local densities of states at mesoscopic scales of random band matrices of width $W$ in dimension $2$. As a result, we show that the local densities of states are alternately positively and negatively correlated in the diffusive regime $O(\log(L/W))$ times, $L$ being the size of he system.