Abstract
We consider the spreading of a wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of the non-ergodic extended states . We show that although non-trivial fractal dimensions characterize wave function statistics in this region, the wave packet spreading is governed by the “diffusion” exponent outside the ballistic regime and in the ballistic regime for . This demonstrates that the multifractality appears only in local quantities like the wave packet survival probability but not in the large-distance spreading of the wave packet.
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