Disturbance spreading in incommensurate and quasiperiodic systems

Abstract

The propagation of an initially localized excitation in one-dimensional incommensurate, quasiperiodic and random systems is investigated numerically. It is discovered that the time evolution of variances σ2(t) of atom displacements depends on the initial condition. For the initial condition with nonzero momentum, σ2(t) goes as tα with α=1 and 0 for incommensurate Frenkel-Kontorova model at V below and above Vc respectively, and α=1 for uniform, quasiperiodic and random chains. It is also found that α=1-β with β the exponent of distribution function of frequency at zero frequency, i.e., ρ(ω)∼ωβ (as ω→0). For the initial condition with zero momentum, α=0 for all systems studied. The underlying physical meaning of this diffusive behavior is discussed. ©2000 The American Physical Society.