S-matrix pole symmetries for non-Hermitian scattering Hamiltonians

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dc.contributor.authorSimon, M. A.
dc.contributor.authorBuendi­a, A.
dc.contributor.authorKiely, Anthony
dc.contributor.authorMostafazadeh, Ali
dc.contributor.authorMuga, Juan Gonzalo
dc.contributor.funderEusko Jaurlaritzaen
dc.contributor.funderMinisterio de Economía, Industria y Competitividad, Gobierno de Españaen
dc.contributor.funderTürkiye Bilimler Akademisien
dc.date.accessioned2019-08-21T14:35:31Z
dc.date.available2019-08-21T14:35:31Z
dc.date.issued2019-05-13
dc.date.updated2019-08-21T14:27:08Z
dc.description.abstractThe 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.en
dc.description.sponsorshipEusko Jaurlaritza (Basque Country Government (Grant No. IT986-16)); Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO/FEDER,UE (Grant No. FIS2015-67161-P)); Türkiye Bilimler Akademisi (Turkish Academy of Sciences (Türkiye Bilimler Akademisi) through its membership grant)en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationSimón, 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.99.052110en
dc.identifier.doi10.1103/PhysRevA.99.052110en
dc.identifier.endpage12en
dc.identifier.issn1050-2947
dc.identifier.issued5en
dc.identifier.journaltitlePhysical Review Aen
dc.identifier.startpage1en
dc.identifier.urihttps://hdl.handle.net/10468/8371
dc.identifier.volume99en
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.urihttps://link.aps.org/doi/10.1103/PhysRevA.99.052110
dc.rights© 2019 American Physical Societyen
dc.subjectEigenvalues and eigenfunctionsen
dc.subjectPolesen
dc.subjectAntilinear operatorsen
dc.subjectComplex conjugatesen
dc.subjectComplex eigenvaluesen
dc.subjectImaginary axisen
dc.subjectNon-Hermitian Hamiltoniansen
dc.subjectPole structuresen
dc.subjectScattering propertyen
dc.subjectStructureless particlesen
dc.subjectHamiltoniansen
dc.titleS-matrix pole symmetries for non-Hermitian scattering Hamiltoniansen
dc.typeArticle (peer-reviewed)en
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