Density-Density Correlators in Infinite Random Matrices

Using the BRM theory developed recently by Fyodorov and Mirlin we calculate the density-density correlators for Banded Random Matrix of infinite size. Within the accuracy of $1\mathrm{/}{b}^2$ ($b$ is the matrix bandwidth) it appears to be the same in both cases of orthogonal and unitary symmetry. Moreover, its form coincides exactly with the formula obtained long ago by Gogolin for electron density-density correlator in strictly 1D disordered metals. In addition to the fixed energy'' density-density correlator considered in the solid state physics we calculate also the time averaged’’ one, which has different properties at small separations. Our predictions are compared with the existing numerical data.