Zero width resonance (spectral singularity) in a complex PT-symmetric potential

Abstract

We show that the complex PT-Symmetric potential, $V(x)=-V_1{sech}^{2}x+i{V}_{2}sechx\tanh x,$, entails a single zero-width resonance (spectral singularity) when $V_1+|V_2|=4n^2+4n+\frac{3}{4}(n=1,2,\mathrm{3..},|V_2|>|V_1|+\frac{sgn(V_1)}{4})$ and the positive resonant energy is given as $E_{\ast }=\frac{1}{4}[|V_2|-(1/4+V_1)]$.

No figures, 4 pages

References in corpus (1)

• Visualization of Branch Points in PT-Symmetric Waveguides

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