Stekloff Eigenvalues in Inverse Scattering

Two-Scale Convergence of Stekloff Eigenvalue Problems in Perforated Domains

By means of the two-scale convergence method, we investigate the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eigenfunctions which improves the understanding of the asymptotic behavior of eigenfunctions. It is also justified that the natural ...

Transmission eigenvalues in inverse scattering theory

In the past few years transmission eigenvalues have become an important area of research in inverse scattering theory with active research being undertaken in many parts of the world. Transmission eigenvalues appear in the study of scattering by inhomogeneous media and are closely related to non-scattering waves. Such eigenvalues provide information about material properties of the scattering m...

The Factorization Method Is Independent of Transmission Eigenvalues

As a rule of thumb, sampling methods for inverse scattering problems suffer from interior eigenvalues of the obstacle. Indeed, throughout the history of such algorithms one meets the phenomenon that if the wave number meets some resonance frequency of the scatterer, then those methods can only be shown to work under suitable modifications. Such modifications often require a-priori knowledge, co...

Inverse scattering theory and transmission eigenvalues

Integrabilty and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is reexamined in the context of the Quantum Inverse Scattering Method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators i...