Diffusive, super-diffusive and ballistic transport in the long-range correlated 1D Anderson model

In this paper, we study the 1D Anderson model with long-range correlated on-site energies. This diagonal-correlated disorder is considered in such a way that the random sequence of site energies εn has a 1/kα power spectrum, where k is the wave-vector of the modulations on the random sequence landscape. Using the Runge–Kutta method to solve the time-dependent Schrödinger equation, we compute the participation number and the Shannon entropy for an initially localized wave packet. We observe that strong correlations can induce ballistic transport associated with the emergence of low-energy extended states, in agreement with previous works in this model. We further identify an intermediate regime with super-diffusive spreading of the wave-packet.