Quantum dynamics in quasiperiodic 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) approximately 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 lambda =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.