Spectral singularities and Bragg scattering in complex crystals

TL;DR

This paper explores the relationship between spectral singularities in non-Hermitian complex crystals and Bragg scattering, revealing how spectral singularities influence scattering processes in PT-symmetric systems.

Contribution

It establishes an equivalence between spectral singularities and secularities in Bragg diffraction, and analyzes their signatures in wave packet scattering in PT-symmetric complex crystals.

Findings

Spectral singularities can cause secularities in Bragg diffraction patterns.

Signatures of spectral singularities are observable in wave packet scattering.

The study links spectral singularities with observable scattering phenomena in complex crystals.

Abstract

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.