金平均和银平均Labyrth Tilings中波包动力学的重整化群方法
Renormalization Group Approach for the Wave Packet Dynamics in Golden-Mean and Silver-Mean Labyrinth Tilings
摘要：
研究了一维、二维和三维准周期紧束缚模型中的量子扩散。首先，我们研究了一类一维准周期链，其中原子通过强弱键耦合，并按照金属平均序列排列。相关的广义迷宫平铺在d维，然后从直接产品的d这样的链，这使我们能够考虑相当大的系统数值。通过计算波包均方位移随时间的标度行为，研究了电子输运。结果表明，在这些系统中的异常扩散的发生。通过扩展一个重整化群的方法，最初提出的黄金平均链，我们还显示了银平均链以及高维迷宫平铺，在政权的强准周期调制的波包动力学是由潜在的准周期结构。
英文摘要：
We study the quantum diffusion in quasiperiodic tight-binding models in one, two, and three dimensions. First, we investigate a class of one-dimensional quasiperiodic chains, in which the atoms are coupled by weak and strong bonds aligned according to the metallic-mean sequences. The associated generalized labyrinth tilings in d dimensions are then constructed from the direct product of d such chains, which allows us to consider rather large systems numerically. The electronic transport is studied by computing the scaling behavior of the mean-square displacement of the wave packets with respect to the time. The results reveal the occurrence of anomalous diffusion in these systems. By extending a renormalization group approach, originally proposed for the golden-mean chain, we show also for the silver-mean chain as well as for the higher-dimensional labyrinth tilings that in the regime of strong quasiperiodic modulation the wave-packet dynamics are governed by the underlying quasiperiodic structure.
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