S-matrix pole symmetries for non-Hermitian scattering Hamiltonians
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Date
2019-05-13
Authors
Simon, M. A.
Buendia, A.
Kiely, Anthony
Mostafazadeh, Ali
Muga, Juan Gonzalo
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American Physical Society
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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) possessing 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 on the 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.
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Keywords
Eigenvalues and eigenfunctions , Poles , Antilinear operators , Complex conjugates , Complex eigenvalues , Imaginary axis , Non-Hermitian Hamiltonians , Pole structures , Scattering property , Structureless particles , Hamiltonians
Citation
Simón, M. A., Buendía, A., Kiely, A., Mostafazadeh, A. and Muga, J. G. (2019) 'S-matrix pole symmetries for non-Hermitian scattering Hamiltonians', Physical Review A, 99(5), 052110 (12 pp). doi: 10.1103/PhysRevA.99.052110
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© 2019 American Physical Society