Power spectrum characterization of the Anderson transition

We examine the power spectrum of the energy level fluctuations of a family of critical power-law random banded matrices whose spectral properties are similar to those of a disordered conductor at the Anderson transition. It is shown analytically and numerically that at the Anderson transition the power spectrum presents 1∕f² noise for small frequencies but 1∕f noise for larger frequencies. The analysis of the region between these two power-law limits gives an accurate estimation of the Thouless energy of the system. Finally we discuss in what circumstances these findings may be relevant in the case of nonrandom Hamiltonians.