Quantum diffusion in the generalized Harper equation

We study numerically the dynamic and spectral properties of a one-dimensional quasi-periodic system, where site energies are given by ∈_k = V cos 2π f cursive Greek chi_k with cursive Greek chi_k denoting the kth quasiperiodic lattice site. When 2π f is given by the reciprocal lattice vector G(m, n) with n and m being successive Fibonacci numbers, the variance of the wavepacket is found to grow quadratically in time, regardless of the potential strength V. For other values of f, there exists a critical value of V beyond which the growth of the wavepacket variance is bounded. In particular an anomalous diffusion takes place for 2π f corresponding to G(m, n) with generic integers m and n. The level-spacing distribution is also examined, and the corresponding exponent β is observed to decrease with V.