1,721,093 research outputs found
Zero Modes and Low-Energy Resolvent Expansion for Three Dimensional Schrödinger Operators with Point Interactions
No full text
Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range
No full textWe 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
The tectonic setting of Mount Vesuvius and the correlation between its eruptions and the earthquakes of the Southern Apennines
No full textMount Vesuvius is emplaced on a regional NE-SW-trending fault that accommodates the stretching of the lithosphere caused by a backward retreat of the Calabrian arc. The dynamics of the Calabrian arc controls the temporal occurrence of earthquakes in the Southern Apennines and in Sicily. By means of a detailed statistical approach, we identified a significant correlation between seismic events occurring in different subsets of this geodynamic domain: seismicity changes in the Southern Apennines follow those in the Calabrian arc after 18-21 years, while seismicity changes in Sicily follow those in the Calabrian arc after 8-10 years. The seismicity changes in these three areas appear also to have affected the eruptive activity of Vesuvius in the period 1631-1944. The major effusive-explosive eruptions of this period followed the seismicity changes in the Southern Apennines after 6-13 years and those in the Calabrian arc after 36-39 years. From a tectonic point of view, this indicates a direct link between the eruptive activity of Vesuvius and the dynamics of the Calabrian arc. The backward retreat of the arc produces strain pulses propagating to adjacent areas. From a volcanological point of view, we speculate that the arrival of an extension strain pulse in the area of Vesuvius may trigger the fast movement of magma-filled cracks that stay in unstable equilibrium in the roots of the volcano. © 1993
Singular Hartree equation in fractional perturbed Sobolev spaces
No full textWe establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space
Schrödinger Flow’s Dispersive Estimates in a regime of Re-scaled Potentials
No full textThe problem of monitoring the (constants in the estimates that quantify the) dispersive behaviour of the flow generated by a Schrödinger operator is posed in terms of the scaling parameter that expresses the small size of the support of the potential, along the scaling limit towards a Hamiltonian of point interaction. At positive size, dispersive estimates are completely classical, but their dependence on the short range of the potential is not explicit, and the understanding of such a dependence would be crucial in connecting the dispersive behaviour of the short-range Schrödinger operator with the zero-range Hamiltonian. The general set-up of the problem is discussed, together with preliminary answers, open questions, and plausible conjectures, in a ‘propaganda’ spirit for this subject
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