Spectral singularities and Bragg scattering in complex crystals

2010/01/06 by Stefano Longhi, S. Longhi · 10 citations
Mathematics · Physics and Astronomy · #Bloch wave #Diffraction #Floquet theory #Gravitational singularity #Hermitian matrix #Mathematical analysis #Mathematics #Nonlinear system #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Scattering #Singularity #Wave packet #quant-ph

paper · pdf · doi:10.1103/physreva.81.022102

published as Phys. Rev. A 81, 022102 (2010) · 6 pages, 5 figures, to be published in Phys. Rev. A

arxiv created 2010/01/06 · openalex publication_date 2010/02/03 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Making sense of non-Hermitian Hamiltonians
• Exceptional Points of Non-hermitian Operators
• Movimientos campesinos en Francia: la Provenza
• Complex periodic potentials with real band spectra
• Association of resonance states with the incomplete spectrum of finite complex-scaled Hamiltonian matrices
• Physics of Nonhermitian Degeneracies

Cited by

• Classical trajectories of the continuum states of the \chem\calPT symmetric Scarf II potential
• Solvable model for solitons pinned to a parity-time-symmetric dipole
• High-directional wave propagation in periodic loss modulated materials
• PT symmetry in a fractional Schrödinger equation
• Perturbative unidirectional invisibility
• Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential
• CPsymmetry in optical systems
• Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations
• Scattering by Finite PeriodicPT-Symmetric Structures
• Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, PT - and supersymmetric potential

Related

• Physics of Spectral Singularities
• Phase transitions and spectral singularities in a class of one-dimensional parity-time-symmetric complex potentials
• Bloch oscillations in complex crystals with PT symmetry
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Non-Hermitian Singularities in Scattering Spectra of Mie Resonators