The geometrical basis of PT symmetry

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dc.contributor.authorSánchez Soto, Luis Lorenzo
dc.contributor.authorMonzón Serrano, Juan José
dc.date.accessioned2023-06-17T13:18:45Z
dc.date.available2023-06-17T13:18:45Z
dc.date.issued2018-10
dc.description© 2018 by the authors. Licensee MDPI, Basel, Switzerland Author Contributions: Both authors contributed equally to all aspects of preparing this manuscript. Funding: Financial support from the Spanish MINECO (Grant No. FIS2015-67963-P) is gratefully acknowledged. Acknowledgments: We acknowledge illuminating discussions with José María Montesinos. Conflicts of Interest: The authors declare no conflicts of interest.
dc.description.abstractWe reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Mobius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.
dc.description.departmentDepto. de Óptica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Economía y Competitividad (MINECO)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/50675
dc.identifier.doi10.3390/sym10100494
dc.identifier.issn2073-8994
dc.identifier.officialurlhttp://dx.doi.org/10.3390/sym10100494
dc.identifier.relatedurlhttps://www.mdpi.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/12995
dc.issue.number10
dc.journal.titleSymmetry
dc.language.isoeng
dc.publisherMDPI
dc.relation.projectIDFIS2015-67963-P
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/es/
dc.subject.cdu535
dc.subject.keywordNon-hermitian hamiltonians
dc.subject.keywordComplex periodic potentials
dc.subject.keywordQuantum-mechanics
dc.subject.keywordPt-symmetry
dc.subject.keywordEigenvalues
dc.subject.keywordEquivalent
dc.subject.keywordScattering
dc.subject.keywordSpectra
dc.subject.ucmÓptica (Física)
dc.subject.unesco2209.19 Óptica Física
dc.titleThe geometrical basis of PT symmetry
dc.typejournal article
dc.volume.number10
dspace.entity.typePublication
relation.isAuthorOfPublication88b797ff-cbd7-4498-a9c7-4e39f4fa4776
relation.isAuthorOfPublication4d5601ee-f965-4904-ae2e-2f1515a3f669
relation.isAuthorOfPublication.latestForDiscovery88b797ff-cbd7-4498-a9c7-4e39f4fa4776

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