Correlations of the local density of states in quasi-one-dimensional wires

We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric sigma model, we obtain the full dependence of the two-point correlation function on the distance between the points. In the limit of zero energy difference, our calculation reproduces the statistics of a single localized wave function. At logarithmically large distances of the order of the Mott scale, we obtain a reentrant behavior similar to that in strictly one-dimensional chains.

Figure 1

(Color online) Dependence of the LDOS correlation function $R\left(\omega ,x\right)$ on $t=x/\xi$ for various values of $\omega /{\Delta }_{\xi }$ shown on the graph.