Quantum mechanical relaxation of open quasiperiodic systems

Details Quantum mechanical relaxation of open quasiperiodic systems Quantum mechanical relaxation of open quasiperiodic systems

2001-02-14

arxiv.org/abs/cond-mat/0102256v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevB.64.224210

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 $t^*\sim L^{\gamma}$, 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.

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