Scattering by many small inhomogeneities and applications - Ramm, Alexander G. (World Scientific, 2011)
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’s equation described by a desired potential. Similar ideas were developed by the author for acoustic and electromagnetic (EM) wave scattering problems.
Keywords: Wave scattering by small inhomogeneities; Metamaterials; Nanotechnology; Refraction coefficient; Negative refraction