PT-symmetric waveguides

Details PT-symmetric waveguides PT-symmetric waveguides

2007-07-20

arxiv.org/abs/0707.3039v2

Integral Equations Operator Theory 62 (2008), no. 4, 489-515.

Physics

Mathematical Physics

LaTeX, 25 pages; more detailed description of various types of spectra; version accepted for publication in Integral Equations

Scientific paper

10.1007/s00020-008-1634-1

We introduce a planar waveguide of constant width with non-Hermitian PT-symmetric Robin boundary conditions. We study the spectrum of this system in the regime when the boundary coupling function is a compactly supported perturbation of a homogeneous coupling. We prove that the essential spectrum is positive and independent of such perturbation, and that the residual spectrum is empty. Assuming that the perturbation is small in the supremum norm, we show that it gives rise to real weakly-coupled eigenvalues converging to the threshold of the essential spectrum. We derive sufficient conditions for these eigenvalues to exist or to be absent. Moreover, we construct the leading terms of the asymptotic expansions of these eigenvalues and the associated eigenfunctions.

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