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Open Quantum Systems Decoherence Quantum Simulation

Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies

arXiv

Authors: Ali Mostafazadeh

Year

2009

Paper ID

9130

Status

Preprint

Abstract Read

~2 min

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Abstract

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a wave guide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic wave guide.

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Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0901.4472 [2] arXiv https://arxiv.org/abs/0901.4472 [3] Publisher https://arxiv.org/abs/0901.4472

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