Relation between the Correlation Dimensions of Multifractal Wavefunctions and Spectral Measures in Integer Quantum Hall Systems

Abstract

We study the time evolution of wavepackets of non-interacting electrons in a two-dimensional disordered system in strong magnetic field. For wavepackets 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, $p(t) \sim t^{-D_2/2}$, with a non-conventional exponent $D_2/2$. $D_2$ is the generalized dimension describing the scaling of the second moment of the wavefunction. We show that the corresponding spectral measure is multifractal and that the exponent $D_2/2$ equals the generalized dimension $\widetilde{D}_2$ of the spectral measure.