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) is similar to t-D2/2, 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 D2 of the spectral measure.