Dynamics of an Electron in Quasiperiodic Systems. I. Fibonacci Model

Abstract

Dynamics of an electron in quasiperiodic systems is studied numerically. Calculations are carried out for the one-dimensional tight-binding model with diagonal or off-diagonal modulation obeying the Fibonacci sequence. The width of the wavepacket of an electron put on a single site at time t =0 exhibits such an overall time evolution as \(\sqrt{\langle\varDelta x^{2}\rangle}\sim t^{\alpha}\) (0<α<1). The dynamical index α decreases continuously with increasing the modulation strength. This anomalous power-law diffusion is successfully interpreted in terms of renormalization group arguments in both the strong and weak modulation limits.