Abstract
We investigate the properties of two anti-parity-time (anti-PT )-symmetric four-site scattering centers. The anti-PT -symmetric scattering center may have imaginary couplings, real couplings, and real on-site potentials. The only difference between the two scattering centers is the coupling between two central sites of the scattering center, which plays a crucial role in determining the parity of anti-PT symmetry and significantly affects the scattering properties. For the imaginary coupling, the even-parity anti-PT -symmetric scattering center possesses nonunitary scattering and the difference between the reflection and transmission is unity; for the real coupling, the odd-parity anti-PT -symmetric scattering center possesses unitary scattering and the sum of the reflection and transmission is unity. The coupling-induced different scattering behaviors are verified in the numerical simulations. Our findings reveal that a significant difference in the dynamics can be caused by a slight difference between two similar anti-PT -symmetric non-Hermitian scattering centers.
Highlights
In quantum mechanics, the Hermitian Hamiltonian of a quantum system ensures the real energy spectrum and the conservation of a probability current
Our findings reveal that a significant difference in the dynamics can be caused by a slight difference between two similar anti-PT -symmetric non-Hermitian scattering centers
The nonorthogonal eigenstate and nonunitary time evolution [20–23], eigenstate coalescence and exceptional point (EP) enhanced sensing [24–28], and the exotic topology of EPs have been predicted and successfully demonstrated in many experimental platforms [29–35]; realization in the quantum regime [36,37]. These have boosted the development of the complex extension of quantum mechanics and greatly deepen our understanding of non-Hermitian systems—research interest in non-Hermitian systems continuously increases in the material, engineering, and physics science
Summary
The Hermitian Hamiltonian of a quantum system ensures the real energy spectrum and the conservation of a probability current. Non-Hermitian parity-time (PT ), symmetric Hamiltonians can possess real spectra [1–6] and have been experimentally realized in many different physical systems [7–13]. If the central coupling is imaginary, the four-site scattering center has even-parity antiPT -symmetry, the scattering is nonunitary, and the reflection (R) and transmission (T ) satisfy R − T = 1. If the central coupling is real, the four-site scattering center has odd-parity anti-PT -symmetry, the scattering is unitary, and the reflection and transmission satisfy R + T = 1 even though the scattering center is non-Hermitian.
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