Quantitative spectral analysis of electromagnetic scattering. II: Evolution semigroups and non-perturbative solutions

TL;DR

This paper develops a non-perturbative method for electromagnetic scattering based on the stability of an evolution semigroup related to the Green operator, enhancing the classical Born approximation.

Contribution

It introduces a novel approach using evolution semigroup stability to solve scattering problems non-perturbatively, advancing beyond traditional Born approximation methods.

Findings

Established strong stability of the evolution semigroup on polynomial compactness.

Proposed a non-perturbative solution method for light scattering.

Improved accuracy over the classical Born approximation.

Abstract

We carry out quantitative studies on the Green operator $ \hat{\mathscr G}$ associated with the Born equation, an integral equation that models electromagnetic scattering, building the strong stability of the evolution semigroup $\{\exp(-i\tau\hat{\mathscr G})|\tau\geq0\} $ on polynomial compactness and the Arendt-Batty-Lyubich-V\~u theorem. The strongly-stable evolution semigroup inspires our proposal of a non-perturbative method to solve the light scattering problem and improve the Born approximation.