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

Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range

Scandone R
2019

Abstract

We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrodinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonancedriven 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 zeroenergy resonance for Schrodinger operators formed by a fractional Laplacian and a regular potential.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/901005
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