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    Hermitian scattering behavior for the non-Hermitian scattering center

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    We study the scattering problem for the non-Hermitian scattering center, which consists of two Hermitian clusters with anti-Hermitian couplings between them. Counterintuitively, it is shown that it acts as a Hermitian scattering center, satisfying r2+t2=1|r| ^{2}+|t| ^{2}=1, i.e., the Dirac probability current is conserved, when one of two clusters is embedded in the waveguides. This conclusion can be applied to an arbitrary parity-symmetric real Hermitian graph with additional PT-symmetric potentials, which is more feasible in experiment. Exactly solvable model is presented to illustrate the theory. Bethe ansatz solution indicates that the transmission spectrum of such a cluster displays peculiar feature arising from the non-Hermiticity of the scattering center.Comment: 6 pages, 2 figure