Multipoint scatterers with bound states at zero energy

Abstract

We study multipoint scatterers with zero-energy bound states in three dimensions. We present examples of such scatterers with multiple zero eigenvalue or with strong multipole localization of zero-energy bound states.

Construction of bimetallic FeCo–SA/DABCO nanosheets by modulating the electronic structure for improved electrocatalytic oxygen evolution

“…The more active the metal element, and the poorer its capacity to attract electrons, the bigger the nonmetal element's electronegativity; this was consistent with the fact that the XPS peak for FeCo-SA/DABCO changes to higher binding energy. [46][47][48] Previous research revealed that in transition metal monosulfides, the S 2p XPS peak appears as a quasi-single peak, but in disulfides, the existence of an equal intensity doublet is a distinct peak. According to Fig.…”

Transmission eigenvalues for multipoint scatterers

“…It is important that for the multipoint scatterers the scattering eigenfunctions and scattering amplitudes are calculated explicitly (see, for example, [2,15,16]). Let…”

“…. , n, the strength ε j of the point scatterer ε j δ(x − y j ) in (1.2) is encoded by a real parameter α j ; see, also, for example, [2,16].…”

“…These "renormalized" δ-functions for d = 2, 3 are known as Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev-type point scatterers. Exact definitions for the multipoint scatterers in dimensions d = 2, 3 can be found in [2,15,16]. Historically, mathematical definitions of point scatterers in dimension d = 3 go back to [5,4].…”

“…. , n, the strength ε j of the point scatterer ε j δ(x − y j ) in (1.2) is encoded by α j , see, for example, [2,16]. If α j = ∞, then ǫ j = 0 (and the corresponding single point scatterer vanishes).…”