Fluctuations of the number of energy levels at the mobility edge

We present a detailed analysis of the behavior of the two-level correlation function R(s) in the disordered sample. We show that in the vicinity of the Anderson transition as well as in two dimensions, the variance of the number of levels in an energy band of a width E has a linear behavior as a function of E. This is related with an ‘‘anomalous’’ contribution to the sum rule for R(s), which comes from the ‘‘ballistic’’ region of s.