论文标题
分数可饱和杂质
The fractional saturable impurity
论文作者
论文摘要
我们通过分析和数值检查分数对嵌入一维晶格中的饱和体积和表面杂质的影响。我们使用先前引入的分数拉普拉斯，并且通过使用晶格绿色功能，我们能够获得界限的状态能量和振幅曲线，这是分数指数$ s $ s $ s $ s $ s $ s $ s $ s $ sumberity grount $χ$的函数，用于表面和散装杂质。该变速箱以$ s $和$χ$的函数为封闭形式获得，在小部分指数值下显示出与标准案例的强大偏差。对于批量和表面模式，最初定位的激发的自我捕获在质量上相似，但是在所有情况下，在$ s \ rightarrow 0 $上获得完全限制，如理论上和数值上所示。
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.
