B. Huckestein et L. Schweitzer, RELATION BETWEEN THE CORRELATION DIMENSIONS OF MULTIFRACTAL WAVE-FUNCTIONS AND SPECTRAL MEASURES IN INTEGER QUANTUM HALL SYSTEMS, Physical review letters, 72(5), 1994, pp. 713-716
We study the time evolution of wave packets of noninteracting electron
s 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 probabil
ity 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 dimensio
n 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.