We study the time evolution of the survival probability P(t) in open
one-dimensional quasiperiodic tight-binding samples of size L, at critical
conditions. We show that it decays algebraically as P(t)∼t−α up
to times t∗∼Lγ, where α=1−D0E, γ=1/D0E and
D0E is the fractal dimension of the spectrum of the closed system. We
verified these results for the Harper model at the metal-insulator transition
and for Fibonacci lattices. Our predictions should be observable in propagation
experiments with electrons or classical waves in quasiperiodic superlattices or
dielectric multilayers.Comment: 4 pages, 5 figure