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Complex potential and non-Hermitian hopping amplitude are building blocks ofa non-Hermitian quantum network. Appropriate configuration, such asPT-symmetric distribution, can lead to the full real spectrum. To investigatethe underlying mechanism of this phenomenon, we study the phase diagram of asemi-infinite non-Hermitian system. It consists of a finite non-Hermitiancluster and a semi-infinite lead. Based on the analysis of the solution of theconcrete systems, it is shown that it can have the full real spectrum withoutany requirements on the symmetry and the wave function within the lead becomesa unidirectional plane wave at the exceptional point. This universal dynamicalbehavior is demonstrated as the persistent emission and reflectionlessabsorption of wave packets in the typical non-Hermitian systems containing thecomplex on-site potential and non-Hermitian hopping amplitude.

Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point