Spectral singularities and Bragg scattering in complex crystals

By S. Longhi. 2010

153 citations recorded by the source corpus.

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 $\mathcal{P}\mathcal{T}$-symmetric complex crystal.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2a7c56f9b32c63c11f2db1adf589616cd8c339df

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

PT symmetry in a fractional Schrödinger equation (2016, methodology): “5 can also be derived analytically, based on the method previously applied to the regular Schrödinger equation (α = 2) [36].”
Nonlinear waves in PT -symmetric systems (2016, background): “…known for a number of particular cases, including the step-like potential (35) (Mostafazadeh, 2009b, 2011a, 2014), δ-function potentials (Mostafazadeh and Mehri-Dehnavi, 2009), PT - symmetric Scarff II potentials (Ahmed, 2009), and special types of periodic potentials (Gasymov, 1980; Longhi, 2010).”