  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 $\sigma^2(t)$ of atom
displacements depends on the initial condition. For the initial condition with
nonzero momentum, $\sigma^2(t)$ goes as $t^\alpha$ with $\alpha=1$ and 0 for
incommensurate Frenkel-Kontorova (FK) model at $V$ below and above $V_c$
respectively; and $\alpha=1$ for uniform, quasiperiodic and random chains. It
is also found that $\alpha=1-\beta$ with $\beta$ the exponent of distribution
function of frequency at zero frequency, i.e., $\rho(\omega)\sim
\omega^{\beta}$ (as $\omega\to 0$). For the initial condition with zero
momentum, $\alpha=0$ for all systems studied. The underlying physical meaning
of this diffusive behavior is discussed.
