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arXiv · 1109.2187

Hermitian scattering behavior for the non-Hermitian scattering center

L. Jin·Z. Song
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Abstract

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 $|r| ^{2}+|t| ^{2}=1$, 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.

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L. Jin, Z. Song. 2011-09-10. Hermitian scattering behavior for the non-Hermitian scattering center. https://doi.org/10.1103/physreva.85.012111

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