分数饱和杂质
The fractional saturable impurity
摘要：
我们研究分析和数值上的可饱和体和表面杂质嵌入在一个一维晶格分数的效果。我们使用的分数拉普拉斯算子之前介绍了我们，并通过使用晶格格林函数，我们能够获得的束缚态能量和振幅分布，作为分数指数$s$和饱和杂质强度$χ$的函数，表面和体杂质。透射率作为$s$和$χ$的函数以封闭形式获得，在小的分数指数值处显示出与标准情况的强烈偏差。初始本地化激发的自陷是定性相似的体模和表面模，但在所有情况下，在$s\rightarrow 0$得到完整的限制，如理论所示和观察数值。
英文摘要：
We examine analytically and numerically the effect of fractionality on a saturable bulk and surface impurity embedded in a 1D lattice. We use a fractional Laplacian introduced previously by us, and by the use of lattice Green functions we are able to obtain the bound state energies and amplitude profiles, as a function of the fractional exponent $s$ and saturable impurity strength $χ$ for both, surface and bulk impurity. The transmission is obtained in closed form as a function of $s$ and $χ$, showing strong deviations from the standard case, at small fractional exponent values. The selftrapping of an initially-localized excitation is qualitatively similar for the bulk and surface mode, but in all cases complete confinement is obtained at $s\rightarrow 0$, as shown theoretically and observed numerically.
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