Smoothed universal correlations in the two-dimensional Anderson model

We report on calculations of smoothed spectral correlations in the two-dime nsional Anderson model for weak disorder. As pointed out [M. Wilkinson, J. Phys. A: 21, 1173 (1988)], an analysis of the smoothing dependence of the c orrelation functions provides a sensitive means of establishing consistency with random matrix theory. We use a semiclassical approach to describe the se fluctuations and offer a detailed comparison between numerical and analy tical calculations for an exhaustive set of two-point correlation functions . We consider parametric correlation functions with an external Aharonov-Bo hm flux as a parameter and discuss two cases, namely broken time-reversal i nvariance and partial breaking of time-reversal invariance. Three types of correlation functions are considered: density of states, velocity, and matr ix element correlation functions. For the values of the smoothing parameter close to the mean level spacing the semiclassical expressions and the nume rical results agree quite well in the whole range of the magnetic flux. [S0 163-1829(99)11805-8].