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

2009/01/31 by Ali Mostafazadeh · 1 citation
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #quant-ph

paper · pdf · doi:10.1103/physrevlett.102.220402

published as Phys.Rev.Lett.102:220402,2009 · Published version

arxiv created 2010/06/02 · arxiv updated 2010/11/24

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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