Localization in a one-dimensional alloy with an arbitrary distribution of spacing between impurities: Application to Lévy glass,Physical Review E

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Localization in a one-dimensional alloy with an arbitrary distribution of spacing between impurities: Application to Lévy glass
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-21 , DOI: 10.1103/physreve.106.034128
Reza Sepehrinia ₁

Affiliation

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.

中文翻译：

具有任意杂质间距分布的一维合金中的局部化：应用于莱维玻璃

我们已经研究了波在由杂质组成的一维晶格中的局部化，其中连续杂质之间的间距可以在给定概率下取某些值。一般来说，杂质的这种分布会导致无序的相关性。特别是，对于间距的幂律分布，该系统被用作 Lévy 眼镜中光传播的模型。我们介绍了一种计算 Lyapunov 指数的方法，该方法克服了以往研究的局限性，可以很容易地扩展到更高阶的微扰理论。我们获得了四阶微扰的李雅普诺夫指数，并讨论了微扰理论的有效性范围、透明状态和异常能量，这些异常能量的特征是在不同的展开阶中存在分歧。

更新日期：2022-09-21

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