Anomalous Diffusion in Quasi One Dimensional Systems

In order to perform quantum Hamiltonian dynamics minimizing localization effects, we introduce a quasi-one dimensional tight-binding model whose mean free path is smaller than the size of the sample. This one, in turn, is smaller than the localization length. We study the return probability to the starting layer of the system by means of direct diagonalization of the Hamiltonian. We create a one dimensional excitation and observe sub-diffusive behavior for times larger than the Debye time but shorter than the Heisenberg time. The exponent corresponds to the fractal dimension $d^{*} \sim 0.72$ which is compared to that calculated from the eigenstates by means of the inverse participation number.