Fractal dynamics of electron wave packets in one-dimensional quasiperiodic systems

Abstract

The dynamics of an electron described by the one-dimensional tight-binding Hamiltonian with quasiperiodic (Fibonacci) modulation is studied numerically. The width of an initially localized wave packet is found to increase with time t in an overall power-law form \ensuremath{\sim}${t}^{\ensuremath{\alpha}}$ (0<\ensuremath{\alpha}<1). The exponent \ensuremath{\alpha} continuously decreases with increasing strength of quasiperiodic modulation. Moreover, prominent hierarchical oscillations are found to occur in the case of strong modulation. These results are explained well by a renormalization-group argument.