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Coherent perfect absorption with and without lasing in complex potentials

We prove that coherent perfect absorption (CPA) without lasing is {\bf not} possible in the PT-symmetric domain as the s-matrix is such that $|\det S(\pm k)|=1$. We study coherent scattering from three complex potentials, one solved analytically and the other two numerically. We conjecture that in the domain of unbroken symmetry (when the potential has real discrete spectrum) neither spectral singularity nor CPA can occur. We show that Scarf II potential is a special model that can analytically and explicitly exhibit these as well as other novel phenomena and their subtleties. \pacs{03.65-w, 03.65.Nk, 11.30.Er, 42.25.Bs, 42.79.Gn