Hermitian scattering behavior for the non-Hermitian scattering center

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.

6 pages, 2 figures

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Cited by in corpus (18)

• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Reciprocal and unidirectional scattering of parity-time symmetric structures
• Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• Probability-preserving evolution in a non-Hermitian two-band model
• Transport properties in a Non-Hermitian triple-quantum-dot structure
• Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Coupling-induced nonunitary and unitary scattering in anti-PT-symmetric non-Hermitian systems
• Unitary Scattering Protected by Pseudo-Hermiticity
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• Single-photon scattering controlled by an imperfect cavity