Multifractal quantum evolution at a mobility edge

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Abstract
We describe the time evolution of a quantum wavepacket at the Anderson metal-insulator transition using a quasirandom model as an example of a system with a mobility edge. It is demonstrated that the dynamical wavefunction is multifractal characterized by a continuous set of generalized spectral dimensions mu (q) and we find its ( alpha - f( alpha ) spectra. We also define and calculate an infinite hierarchy of diffusion exponents gamma (q) corresponding to all the displacement moments ( mod r(t) mod q) describing the quantum evolution. A slow subdiffusive decay for the 'staying at the origin probability' (P(t)) averaged over all initial sites is obtained at the mobility edge.