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dc.contributor.authorBallesteros Castañeda, Ángel 
dc.contributor.authorGutiérrez Sagredo, Iván 
dc.date.accessioned2023-03-01T08:44:41Z
dc.date.available2023-03-01T08:44:41Z
dc.date.issued2023-03
dc.identifier.issn0167-2789
dc.identifier.urihttp://hdl.handle.net/10259/7471
dc.description.abstractThe so-called Darboux III oscillator is an exactly solvable N-dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. This oscillator can be interpreted as a smooth (super)integrable deformation of the usual N-dimensional harmonic oscillator in terms of a non-negative parameter λ which is directly related to the curvature of the underlying space. In this paper, a detailed study of the Shannon information entropy for the quantum version of the Darboux III oscillator is presented, and the interplay between entropy and curvature is analysed. In particular, analytical results for the Shannon entropy in the position space can be found in the N-dimensional case, and the known results for the quantum states of the N-dimensional harmonic oscillator are recovered in the limit of vanishing curvature λ → 0. However, the Fourier transform of the Darboux III wave functions cannot be computed in exact form, thus preventing the analytical study of the information entropy in momentum space. Nevertheless, we have computed the latter numerically both in the one and three-dimensional cases and we have found that by increasing the absolute value of the negative curvature (through a larger λ parameter) the information entropy in position space increases, while in momentum space it becomes smaller. This result is indeed consistent with the spreading properties of the wave functions of this quantum nonlinear oscillator, which are explicitly shown. The sum of the entropies in position and momentum spaces has been also analysed in terms of the curvature: for all excited states such total entropy decreases with λ, but for the ground state the total entropy is minimized when λ vanishes, and the corresponding uncertainty relation is always fulfilled.en
dc.description.sponsorshipThis work has been partially supported by Agencia Estatal de Investigación (Spain) under grant PID2019-106802GB-I00/AEI/ 10.13039/501100011033, by the Regional Government of Castilla y León (Junta de Castilla y León, Spain) and by the Spanish Ministry of Science and Innovation MICIN and the European Union NextGenerationEU/PRTR, as well as the contribution of the European Cooperation in Science and Technology through the COST Action CA18108. The authors acknowledge A. Najafizade for useful discussions at the early stages of this work, and also the Referee for several relevant comments and suggestions.en
dc.format.mimetypeapplication/pdf
dc.language.isoenges
dc.publisherElsevieren
dc.relation.ispartofPhysica D: Nonlinear Phenomena. 2023, V. 445, 133618en
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectShannon entropyen
dc.subjectQuantum informationen
dc.subjectNonlinear oscillatoren
dc.subjectNon-constant curvatureen
dc.subjectDarboux III spaceen
dc.subject.otherFísicaes
dc.subject.otherPhysicsen
dc.subject.otherMatemáticases
dc.subject.otherMathematicsen
dc.titleShannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvatureen
dc.typeinfo:eu-repo/semantics/articlees
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.relation.publisherversionhttps://doi.org/10.1016/j.physd.2022.133618es
dc.identifier.doi10.1016/j.physd.2022.133618
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-106802GB-I00/ES/GRUPO CUANTICOS, GRUPOS DE POISSON-LIE, ESPACIOS HOMOGENEOS Y APLICACIONES/es
dc.relation.projectIDinfo:eu-repo/grantAgreement/COST//CA18108/EU/Quantum gravity phenomenology in the multi-messenger approach/QG-MM/en
dc.journal.titlePhysica D: Nonlinear Phenomenaen
dc.volume.number445es
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersiones


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