Quantum mechanical relaxation of open quasiperiodic systems
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 $P(t)\ensuremath{\sim}{t}^{\ensuremath{-}\ensuremath{\alpha}}$ up to times ${t}^{*}\ensuremath{\sim}{L}^{\ensuremath{\gamma}},$ where $\ensuremath{\alpha}=1\ensuremath{-}{D}_{0}^{E},$ $\ensuremath{\gamma}{=1/D}_{0}^{E},$ and ${D}_{0}^{E}$ is the fractal dimension of the spectrum of the closed system. …