Relation between the correlation dimensions of multifractal wave functions and spectral measures in integer quantum Hall systems

We study the time evolution of wave packets of noninteracting electrons in a two-dimensional disordered system in strong magnetic field. For wave packets built from states near the metal-insulator transition in the center of the lowest Landau band we find that the return probability to the origin p (t) decays algebraically, p (t) t₂^-D/2, with a nonconventional exponent D₂/2. D₂ is the generalized dimension describing the scaling of the second moment of the wave function. We show that the corresponding spectral measure is multifractal and that the exponent D₂/2 equals the generalized dimension D \~{}₂ of the spectral measure.