Spatial Correlations and Multifractality in the Local-Density of States in Disordered Mesoscopic Systems

We consider spatial correlations of local density of states in disordered mesoscopic samples at different length scales. By coarse graining over boxes of size L(b), l less than or similar to L(b) much less than L, we obtain cumulants of the box density of states from these correlations (here l is the mean free path, and L is the sample size). By applying renormalisation group analysis we show that the cumulants are characterised by multifractal behaviour similar to that of inverse participation numbers in an isolated disordered sample.