Exceptional points in real potential scattering

Exceptional points are non-Hermitian degeneracies that appear in parameter-dependent eigenvalue problems, where two or more eigenvalues and their corresponding eigen- vectors coalesce. These types of degeneracies can only be observed in non-Hermitian operators, which leads to the idea that exceptional points are exclusive to open quantum systems. We utilized the dynamical formulation of stationary scattering to study the scattering of waves by two- and three-dimensional finite-length waveg- uides filled with inactive and lossless material. With this formulation, the transfer matrix for these higher-dimensional setups is associated with the pseudo-Hermitian Hamiltonian of a two-level effective quantum system. This Hamiltonian is related to the transfer matrix by a function that exhibits exceptional points. Although these scattering setups are modeled by real potentials, we demonstrate that exceptional points can have a physical effect in these systems. Moreover, we use the compo- sition property of the transfer matrix to solve the scattering problem for a system consisting of multiple finite waveguides and show that exceptional points also have physical realizations at these points.