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

TitlePoint-like perturbed fractional Laplacians through shrinking potentials of finite range
Publication TypePreprint
2018
AuthorsMichelangeli, A, Scandone, R
Document NumberSISSA;16/2018/MATE
InstitutionSISSA

We construct the rank-one, singular (point-like) perturbations of
the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both 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 Schrödinger operators formed by a fractional Laplacian and a regular potential.

http://preprints.sissa.it/handle/1963/35313

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