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

We investigate the local cumulative phases at single sites of the lattice f or time-dependent wave functions in the Anderson model in d=2 and 3. In add ition to a local linear trend, the phases exhibit some fluctuations. We stu dy the time correlations of these fluctuations using detrended fluctuation analysis. Our results suggest that the phase fluctuations are long-range co rrelated, decaying as a power law with time. It seems that the exponent dep ends on the degree of disorder. In d=3, close to the critical disorder Wc=1 6.5, the correlation exponent exhibits a maximum value of alpha approximate to 0.6 which is significantly above random fluctuations (alpha=0.5). (C) 1 999 Published by Elsevier Science B.V. All rights reserved.