Spread of wave packets in disordered hierarchical lattices

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 $1 \tau\sim 1$ and $\langle r^{2}\rangle \propto t^{2}$ in the ballistic regime for $t<\tau\sim 1$ . 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