Publication: On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits
dc.affiliation.dpto | UC3M. Departamento de Matemáticas | es |
dc.affiliation.grupoinv | UC3M. Grupo de Investigación: Análisis Aplicado | es |
dc.contributor.author | Balmaseda Martín, Ángel Aitor | |
dc.contributor.author | Di Cosmo, Fabio | |
dc.contributor.author | Pérez Pardo, Juan Manuel | |
dc.contributor.funder | Comunidad de Madrid | es |
dc.contributor.funder | Ministerio de Economía y Competitividad (España) | es |
dc.date.accessioned | 2021-02-25T12:16:03Z | |
dc.date.available | 2021-02-25T12:16:03Z | |
dc.date.issued | 2019-08-14 | |
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 | en |
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 . | en |
dc.format.extent | 25 | |
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. | en |
dc.identifier.doi | https://doi.org/10.3390/sym11081047 | |
dc.identifier.publicationfirstpage | 1 | |
dc.identifier.publicationissue | 8 | |
dc.identifier.publicationlastpage | 21 | |
dc.identifier.publicationtitle | Symmetry | en |
dc.identifier.publicationvolume | 11 | |
dc.identifier.uri | https://hdl.handle.net/10016/32031 | |
dc.identifier.uxxi | AR/0000026629 | |
dc.language.iso | eng | en |
dc.publisher | MDPI | en |
dc.relation.projectID | Gobierno de España. MTM2017-84098-P | es |
dc.relation.projectID | Comunidad de Madrid. P2018/TCS-4342 | es |
dc.rights | © 2019 by the authors. Licensee MDPI, Basel, Switzerland. | en |
dc.rights | Atribución 3.0 España | * |
dc.rights.accessRights | open access | en |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.subject.eciencia | Matemáticas | es |
dc.subject.other | Groups of symmetry | en |
dc.subject.other | Self-adjoint extensions | en |
dc.subject.other | Quantum circuits | en |
dc.title | On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits | en |
dc.type | research article | * |
dc.type.hasVersion | VoR | * |
dspace.entity.type | Publication |
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