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arXiv · 1803.10191

Point-like perturbed fractional Laplacians through shrinking potentials of finite range

Alessandro Michelangeli·Raffaele Scandone
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Abstract

We reconstruct the rank-one, singular (point-like) perturbations of the $d$-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schr\"{o}dinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both the possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schr\"{o}dinger operators formed by a fractional Laplacian and a regular potential.

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Alessandro Michelangeli, Raffaele Scandone. 2018-03-27. Point-like perturbed fractional Laplacians through shrinking potentials of finite range. https://arxiv.org/abs/1803.10191

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