Are the phases in the Anderson model long-range correlated?

We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d=2 and 3. In addition to a local linear trend, the phases exhibit some fluctuations. We study the time correlations of these fluctuations using detrended fluctuation analysis. Our results suggest that the phase fluctuations are long-range correlated, decaying as a power law with time. It seems that the exponent depends on the degree of disorder. In d=3, close to the critical disorder wc=16.5, the correlation exponent exhibits a maximum value of α≈0.6 which is significantly above random fluctuations (α=0.5).