Point-like perturbed fractional Laplacians through shrinking potentials of finite range
Functional Analysis
2018-04-04 v2 Mathematical Physics
math.MP
Abstract
We reconstruct the rank-one, singular (point-like) perturbations of the -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.
Keywords
Cite
@article{arxiv.1803.10191,
title = {Point-like perturbed fractional Laplacians through shrinking potentials of finite range},
author = {Alessandro Michelangeli and Raffaele Scandone},
journal= {arXiv preprint arXiv:1803.10191},
year = {2018}
}