Spread of wave packets in disordered hierarchical lattices

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 1 > γ > 2. We show that although non-trivial fractal dimensions 0 > Dq = 2-γ > 1 characterize wave function statistics in this region, the wave packet spreading 〈r2〉 ∞ t2 is governed by the diffusion exponent β = 1 outside the ballistic regime t < τ ∼ 1 and 〈r2〉 ∞ t2 in the ballistic regime for t > τ ∼ 1. This emonstrates 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. © EPLA, 2017.