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

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dc.contributor.author Balmaseda Martín, Ángel Aitor
dc.contributor.author Cosmo, Fabio Di
dc.contributor.author Pérez Pardo, Juan Manuel
dc.date.accessioned 2021-02-25T12:16:03Z
dc.date.available 2021-02-25T12:16:03Z
dc.date.issued 2019-08-14
dc.identifier.bibliographicCitation Balmaseda, 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.
dc.identifier.uri http://hdl.handle.net/10016/32031
dc.description.abstract An 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-Text
dc.description.sponsorship The 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 .
dc.format.extent 25
dc.language.iso eng
dc.publisher MDPI
dc.rights © 2019 by the authors. Licensee MDPI, Basel, Switzerland.
dc.rights Atribución 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by/3.0/es/
dc.subject.other Groups of symmetry
dc.subject.other Self-adjoint extensions
dc.subject.other Quantum circuits
dc.title On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.3390/sym11081047
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2017-84098-P
dc.relation.projectID Comunidad de Madrid. P2018/TCS-4342
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 8
dc.identifier.publicationlastpage 21
dc.identifier.publicationtitle Symmetry
dc.identifier.publicationvolume 11
dc.identifier.uxxi AR/0000026629
dc.contributor.funder Comunidad de Madrid
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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