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arXiv · 2209.04074

The fractional saturable impurity

Mario I. Molina
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Abstract

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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Mario I. Molina. 2022-09-09. The fractional saturable impurity. https://doi.org/10.1103/physreva.106.063504

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