Wave propagation in periodic lattices with defects of smaller dimension

TL;DR

This paper develops a method to evaluate the spectrum of discrete periodic operators with lower-dimensional defects, enabling analysis of wave propagation, guided modes, and localized states in physical systems modeled on graphs.

Contribution

It introduces a new procedure for spectral evaluation of perturbed discrete periodic operators with lower-dimensional defects, advancing analysis of wave phenomena in such systems.

Findings

Spectral evaluation method for operators with defects of smaller dimension.

Identification of propagative, guided, and localized spectra.

Application to physical operators on graph structures.

Abstract

The procedure of evaluating of the spectrum for discrete periodic operators perturbed by operators of smaller dimensions is obtained. This result allows to obtain propagative, guided, localised spectra for different kind of physical operators on graphs with defects.