QUANTUM DYNAMICS IN QUASI-PERIODIC SYSTEMS

The electronic motion in quasiperiodic systems (the Harper model, the Fibonacci chain, two- and three-dimensional Fibonacci quasilattices) is studied, in the framework of a tight-binding Hamiltonian. The spreading with time of the wavepacket is described in terms of the behaviour of the autocorrelation function C(t). It is found that, in all cases, C(t) similar to t(-delta) For the Harper model with lambda < 2, the motion of the electron is ballistic (delta = 1), which goes against a previous estimate of delta = 0.84. We show that this discrepancy is due to the neglect of a logarithmic contribution in the scaling analysis. For the Harper model with), = 2 and the Fibonacci chain, the motion is non-ballistic with 0 < delta < 1. For the higher-dimensional Fibonacci quasilattices, C(t) exhibits a transition from a ballistic to a non-ballistic behaviour, upon varying the modulation strength of the quasiperiodicity. The relation between C(t) and the fractal dimensions of the spectral measure is also studied.