Scattering by many small inhomogeneities and applications

TL;DR

This paper develops an asymptotic method for solving many-body quantum scattering problems involving numerous small inhomogeneities, enabling the design of systems with desired potentials.

Contribution

It introduces a novel approach to determine the number and intensities of small inhomogeneities to achieve a specified potential in quantum scattering.

Findings

Method for calculating inhomogeneity distribution and intensities

Application to quantum, acoustic, and electromagnetic scattering

Enables designing systems with tailored potentials

Abstract

Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small inhomogeneities per unit volume and their intensities such that embedding of these inhomogeneities in a bounded region results in creating a new system, described by a desired potential. The governing equation for this system is a non-relativistic Schr\"odinger equation described by a desired potential. Similar ideas were developed by the author for acoustic and electromagnetic (EM) wave scattering problems.