Publication:
Exceptional points and pseudo-Hermiticity in real potential scattering

dc.contributor.coauthorLoran, Farhang
dc.contributor.departmentDepartment of Mathematics
dc.contributor.departmentDepartment of Physics
dc.contributor.kuauthorMostafazadeh, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T12:25:50Z
dc.date.issued2022
dc.description.abstractWe employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials. The transfer matrix for these potentials is related to the time-evolution operator for an associated pseudo-Hermitian Hamiltonian operator H which develops an exceptional point for a discrete set of incident wavenumbers. We use the spectral properties of this operator to determine the transfer matrix of these potentials and solve their scattering problem. We apply our general results to explore the scattering of waves by a waveguide of finite length in two dimensions, where the source of the incident wave and the detectors measuring the scattered wave are positioned at spatial infinities while the interior of the waveguide, which is filled with an inactive material, forms a finite rectangular region of the space. The study of this model allows us to elucidate the physical meaning and implications of the presence of the real and complex eigenvalues of Hand its exceptional points. Our results reveal the relevance of the concepts of pseudo-Hermitian operator and exceptional point in the standard quantum mechanics of closed systems where the potentials are required to be real.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue3
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuTÜBİTAK
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TÜBİTAK)
dc.description.sponsorshipTurkish Academy of Sciences (TÜBA)
dc.description.versionPublisher version
dc.description.volume12
dc.identifier.doi10.21468/SciPostPhys.12.3.109
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR03643
dc.identifier.issn2542-4653
dc.identifier.quartileN/A
dc.identifier.scopus2-s2.0-85128210387
dc.identifier.urihttps://doi.org/10.21468/SciPostPhys.12.3.109
dc.identifier.wos782238100011
dc.keywordsScattering
dc.keywordsMatrix
dc.language.isoeng
dc.publisherThe SciPost Foundation
dc.relation.grantno120F061
dc.relation.ispartofSciPost Physics
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/10494
dc.subjectPhysics
dc.titleExceptional points and pseudo-Hermiticity in real potential scattering
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMostafazadeh, Ali
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
local.publication.orgunit2Department of Physics
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