Anomalous diffusion in quasi-one-dimensional systems

In order to perform quantum Hamiltonian dynamics minimizing localization ef fects, we introduce a quasi-one-dimensional tight-binding model whose mean free path is smaller than the size of the sample. This size, in turn, is sm aller than the localization length. We study the return probability to the starting layer using direct diagonalization of the Hamiltonian. We create a one-dimensional excitation and observe sub-diffusive behavior for times la rger than the Debye time but shorter than the Heisenberg time. The exponent corresponds to the fractal dimension d* similar to 0.72 which is compared to that calculated from the eigenstates by means of the inverse participati on number. (C) 2000 Elsevier Science B.V. All rights reserved.