$S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians

Abstract

The complex eigenvalues of some non-Hermitian Hamiltonians, e.g. parity-time symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension) possesing one of four certain symmetries, the poles of the $S$-matrix eigenvalues in the complex momentum plane are symmetric about the imaginary axis, i.e. they are complex-conjugate pairs in complex-energy plane. This applies even to states which are not bounded eigenstates of the system, i.e. antibound or virtual states, resonances, and antiresonances. The four Hamiltonian symmetries are formulated as the commutation of the Hamiltonian with specific antilinear operators. Example potentials with such symmetries are constructed and their pole structures and scattering properties are calculated.

arXiv comment13 pages, 14 figures

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Cited by in corpus (12)

• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Coupling-induced nonunitary and unitary scattering in anti-PT-symmetric non-Hermitian systems
• High-order spectral singularity
• Unitary Scattering Protected by Pseudo-Hermiticity
• On beautiful analytic structure of the S-matrix
• Quantum-optical implementation of non-Hermitian potentials for asymmetric scattering
• Observing S-Matrix Pole Flow in Resonance Interplay: Cold Collisions of Ultracold Atoms in a Miniature Laser-based Accelerator
• Quantifying Algebraic Asymmetry of Hamiltonian Systems
• Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries
• Balancing gain and loss in symmetrised multi-well potentials
• Swanson Hamiltonian: non-PT-symmetry phase