金属平均拟周期系统的广义逆参与数
Generalized Inverse Participation Numbers in Metallic-Mean Quasiperiodic Systems
摘要：
从量子力学的观点来看，准晶的电子特性是由其本征态的性质决定的。研究广义逆参与数$Z_q \sim N^{-D_q(q-1)}$随系统规模$N$的标度行为是获得这些波函数性质信息的一个可行途径。特别是，我们调查$d$维准周期模型的基础上不同的金属平均准周期序列。通过对紧束缚模型的数值计算，得到了一维金属平均链的本征态。高维的解决方案的相关的广义迷宫瓷砖，然后构建的产品的方法从一维的解决方案。数值结果表明，关系$D_q^{d\mathrm{d}} = d D_q^\mathrm{1d}$适用于这些模型。使用迷宫平铺的产品结构，我们证明了这种关系总是满足银平均模型和标度指数接近这个关系的大系统尺寸也为其他金属平均系统。
英文摘要：
From the quantum mechanical point of view, the electronic characteristics of quasicrystals are determined by the nature of their eigenstates. A practicable way to obtain information about the properties of these wave functions is studying the scaling behavior of the generalized inverse participation numbers $Z_q \sim N^{-D_q(q-1)}$ with the system size $N$. In particular, we investigate $d$-dimensional quasiperiodic models based on different metallic-mean quasiperiodic sequences. We obtain the eigenstates of the one-dimensional metallic-mean chains by numerical calculations for a tight-binding model. Higher dimensional solutions of the associated generalized labyrinth tiling are then constructed by a product approach from the one-dimensional solutions. Numerical results suggest that the relation $D_q^{d\mathrm{d}} = d D_q^\mathrm{1d}$ holds for these models. Using the product structure of the labyrinth tiling we prove that this relation is always satisfied for the silver-mean model and that the scaling exponents approach this relation for large system sizes also for the other metallic-mean systems.
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