Wavefunctions, quantum diffusion, and scaling exponents in golden-mean quasiperiodic tilings
Wavefunctions, quantum diffusion, and scaling exponents in golden-mean quasiperiodic tilings
复制标题
黄金均值准周期平铺中的波函数、量子扩散和标度指数
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
M. Schreiber
中科院分区：
文献类型：
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作者：
S. Thiem;M. Schreiber
我们研究了一维、二维和三维准周期紧束缚模型中波函数的性质和波包动力学。一维准周期链中的原子通过按斐波纳契序列排列的弱键和强键耦合。关联的d维准周期瓦片由d个这样的链的直积构成，其产生超三次瓦片或迷宫瓦片。这种方法使我们能够从数值上考虑相当大的系统。我们用重整化群(RG)方法证明了该系统的波函数是多重分形的，并且在强准周期调制下，其性质与系统的结构有关。我们还研究了波包的动力学，以获得有关电子输运性质的信息。特别地，我们研究了波包的返回概率随时间的标度行为。再次应用RG方法，我们证明了在强准周期调制下，返回几率由潜在的准周期结构决定。此外，我们还讨论了波包宽度的标度指数的下界，并提出了绝对连续区域的修正下界。
We study the properties of wavefunctions and the wavepacket dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider fairly large systems numerically. We show that the wavefunctions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wavepackets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wavepacket with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wavepacket and propose a modified lower bound for the absolute continuous regime.