Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments

TL;DR

This paper reviews a transfer matrix approach for stationary scattering in 2D and 3D, highlighting its ability to avoid divergences and design invisible potentials, advancing theoretical scattering methods.

Contribution

It introduces a transfer matrix formulation acting in infinite-dimensional space, addressing divergence issues and enabling the construction of omnidirectionally invisible potentials.

Findings

Transfer matrix formulation avoids ultraviolet divergences.

Constructed complex potentials with perfect invisibility below cutoff.

Provides a unified framework for 2D and 3D scattering analysis.

Abstract

We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in circumventing the ultraviolet divergences one encounters in solving the Lippman-Schwinger equation for delta-function potentials in two and three dimensions. We also use it to construct complex scattering potentials displaying perfect omnidirectional invisibility for frequencies below a freely preassigned cutoff.