论文标题
在一维合金中定位，并在杂质之间进行任意间距分布：应用于莱维玻璃
Localization in a one-dimensional alloy with an arbitrary distribution of spacing between impurities: Application to Lévy glass
论文作者
论文摘要
我们研究了波在一维晶格中的定位，该晶格由杂质组成，在这些杂质中，连续杂质之间的间距可以带有给定概率的某些值。通常，这种杂质的分布会引起该疾病的相关性。特别是在间距的幂律分布中，该系统被用作莱维眼镜中光传播的模型。我们介绍了一种计算Lyapunov指数的方法，该指数克服了以前的研究中的局限性，并且可以很容易地扩展到更高的扰动理论。我们获得了高达第四顺序的Lyapunov指数，并讨论了扰动理论，透明状态和异常能量的有效性范围，这些能量的特征是不同范围内的差异。我们还进行了与我们的分析结果一致的数值模拟。
We have studied the localization of waves in a one-dimensional lattice consisting of impurities where the spacing between consecutive impurities can take certain values with given probabilities. In general, such a distribution of impurities induces correlations in the disorder. In particular with a power-law distribution of spacing, this system is used as a model for light propagation in Lévy glasses. We introduce a method of calculating the Lyapunov exponent which overcomes limitations in the previous studies and can be easily extended to higher orders of perturbation theory. We obtain the Lyapunov exponent up to fourth order of perturbation and discuss the range of validity of perturbation theory, transparent states, and anomalous energies which are characterized by divergences in different orders of the expansion. We also carry out numerical simulations which are in agreement with our analytical results.
