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On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorBalmaseda Martín, Ángel Aitor
dc.contributor.authorDi Cosmo, Fabio
dc.contributor.authorPérez Pardo, Juan Manuel
dc.contributor.funderComunidad de Madrides
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-02-25T12:16:03Z
dc.date.available2021-02-25T12:16:03Z
dc.date.issued2019-08-14
dc.description.abstractAn analysis of the invariance properties of self-adjoint extensions of symmetric operators under the action of a group of symmetries is presented. For a given group G, criteria for the existence of G-invariant self-adjoint extensions of the Laplace&-Beltrami operator over a Riemannian manifold are illustrated and critically revisited. These criteria are employed for characterising self-adjoint extensions of the Laplace&-Beltrami operator on an infinite set of intervals, &;937# , constituting a quantum circuit, which are invariant under a given action of the group Z . A study of the different unitary representations of the group Z on the space of square integrable functions on Omega is performed and the corresponding Z -invariant self-adjoint extensions of the Laplace&-Beltrami operator are introduced. The study and characterisation of the invariance properties allows for the determination of the spectrum and generalised eigenfunctions in particular examples. View Full-Texten
dc.description.sponsorshipThe authors acknowledge partial support provided by the Ministerio de Economía, Industria y Competitividad" research project MTM2017-84098-P and QUITEMAD proyect P2018/TCS-4342 funded by \Comunidad Autónoma de Madrid". A.B. acknowledges financial support by \Universidad Carlos III de Madrid" through Ph.D. program grant PIPF UC3M 01-1819. F.dC. acknowledges financial support by QUITEMAD proyect P2018/TCS-4342 .en
dc.format.extent25
dc.identifier.bibliographicCitationBalmaseda, A. Di Cosmo, F. y Pérez Pardo, J. M. (2019). On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits. Symmetry, 11(8), 1047.en
dc.identifier.doihttps://doi.org/10.3390/sym11081047
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue8
dc.identifier.publicationlastpage21
dc.identifier.publicationtitleSymmetryen
dc.identifier.publicationvolume11
dc.identifier.urihttps://hdl.handle.net/10016/32031
dc.identifier.uxxiAR/0000026629
dc.language.isoengen
dc.publisherMDPIen
dc.relation.projectIDGobierno de España. MTM2017-84098-Pes
dc.relation.projectIDComunidad de Madrid. P2018/TCS-4342es
dc.rights© 2019 by the authors. Licensee MDPI, Basel, Switzerland.en
dc.rightsAtribución 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherGroups of symmetryen
dc.subject.otherSelf-adjoint extensionsen
dc.subject.otherQuantum circuitsen
dc.titleOn Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuitsen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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