Dynamics of an Electron in Quasiperiodic Systems. II. Harper's Model

Abstract

The dynamics of an electron in a one-dimensional tight-binding model with incommensurate sinusoidal modulation (Harper's model) is studied numerically. The width of a wavepacket of an electron put on a single site at the time t =0 exhibits such asymptotic time evolution as \(\sqrt{\langle\varDelta x^{2}\rangle}\sim t^{\alpha}\), where the dynamical index α takes only three values α=1 for V < V c , α=0 for V > V c and α=α c (a value near 1/2) for V = V c , where V is the strength of modulation and V c is the critical value. This behavior is in a striking contrast with that in Fibonacci chains, in which α can take any value between 0 and 1 depending on the modulation strength as shown in our preceding paper [J. Phys. Soc. Jpn. 57 (1988) 230].