Quantum mechanical relaxation of open quasiperiodic systems

Abstract

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 $P(t)\sim t^{-\alpha }$ up to times $t^{\ast }\sim L^{\gamma }$, where $\alpha =1-D_0^E$, $\gamma =1/D_0^E$ and $D_0^E$ 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.

4 pages, 5 figures

References in corpus (1)

• Chaotic Scattering of Microwaves

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