Publication:
Pseudo-Hermitian description of PT-symmetric systems defined on a complex contour

dc.contributor.coauthorN/A
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorMostafazadeh, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T23:23:34Z
dc.date.issued2005
dc.description.abstractWe describe a method that allows for a practical application of the theory of pseudo-Hermitian operators to PT-symmetric systems defined on a complex contour. We apply this method to study the Hamiltonians H = p(2) + x(2) (ix)(v) with v epsilon (-2, infinity) that are defined along the corresponding anti-Stokes lines. In particular, we reveal the intrinsic non-Hermiticity of H for the cases that v is an even integer, so that H = p(2) +/- x(2+v) and give a proof of the discreteness of the spectrum of H for all v epsilon (-2, infinity). Furthermore, we study the consequences of defining a square-well Hamiltonian on a wedge-shaped complex contour. This yields a PT-symmetric system with a finite number of real eigenvalues. We present a comprehensive analysis of this system within the framework of pseudo-Hermitian quantum mechanics. We also outline a direct pseudo-Hermitian treatment of PT-symmetric systems defined on a complex contour which clarifies the underlying mathematical structure of the formulation of PT-symmetric quantum mechanics based on the charge-conjugation operator. Our results provide conclusive evidence that pseudo-Hermitian quantum mechanics provides a complete description of general PT-symmetric systems regardless of whether they are defined along the real line or a complex contour.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue14
dc.description.openaccessYES
dc.description.sponsoredbyTubitakEuN/A
dc.description.volume38
dc.identifier.doi10.1088/0305-4470/38/14/011
dc.identifier.issn0305-4470
dc.identifier.scopus2-s2.0-17044399715
dc.identifier.urihttps://doi.org/10.1088/0305-4470/38/14/011
dc.identifier.urihttps://hdl.handle.net/20.500.14288/11266
dc.identifier.wos228743800016
dc.keywordsQuantum-mechanics
dc.keywordsSquare-well
dc.keywordsCpt-invariance
dc.keywordsHamiltonians
dc.keywordsReality
dc.keywordsSpectrum
dc.language.isoeng
dc.publisherIop Publishing Ltd
dc.relation.ispartofJournal of Physics A: Mathematical and General
dc.subjectPhysics
dc.subjectMathematical physics
dc.titlePseudo-Hermitian description of PT-symmetric systems defined on a complex contour
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMostafazadeh, Ali
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
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