Fractional powers and singular perturbations of quantum differential Hamiltonians

Abstract

We consider the fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators we outline a programme of relevant questions that deserve being investigated.

Published on J. Math. Phys. (2018)

References in corpus (3)

• On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians
• The $L^p$ boundedness of wave operators for the three-dimensional multi-centre point interaction
• Stationary solutions of a fractional Laplacian with singular perturbation

Cited by in corpus (4)

• Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one
• A general review on the NLS equation with point-concentrated nonlinearity
• A characterization of singular Schrödinger operators on the half-line
• Ground states of the planar nonlinear Schrödinger--Newton system with a point interaction