Quantum mechanical relaxation of open quasiperiodic systems

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 find that it decays algebraically as P(t)~t^-α up to times t*~L^γ, where α=1-D₀E, γ=1/D₀E, and D₀E is the fractal dimension of the spectrum of the closed system. These results were obtained for the Harper model at the metal-insulator transition and for Fibonacci lattices, and are supported by a perturbative argument. These relaxation phenomena should be observable in propagation experiments with electrons or classical waves in quasiperiodic superlattices or dielectric multilayers.