2026-04-28T16:24:23Zhttps://riubu.ubu.es/oai/requestoai:riubu.ubu.es:10259/74712023-04-17T09:28:16Zcom_10259.4_2557com_10259_5086com_10259_2604col_10259.4_2558
Ballesteros Castañeda, Ángel
46
600
0000-0003-4085-3094
Gutiérrez Sagredo, Iván
270
600
0000-0002-8607-6609
2023-03-01T08:44:41Z
2023-03-01T08:44:41Z
2023-03
0167-2789
http://hdl.handle.net/10259/7471
10.1016/j.physd.2022.133618
The 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.
This 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.
application/pdf
eng
Elsevier
Physica D: Nonlinear Phenomena. 2023, V. 445, 133618
https://doi.org/10.1016/j.physd.2022.133618
info: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/
info:eu-repo/grantAgreement/COST//CA18108/EU/Quantum gravity phenomenology in the multi-messenger approach/QG-MM/
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
Shannon entropy
Quantum information
Nonlinear oscillator
Non-constant curvature
Darboux III space
Física
Matemáticas
Physics
Mathematics
Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Physica D: Nonlinear Phenomena
445
THUMBNAIL
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oai:riubu.ubu.es:10259/7471
2023-04-17 11:28:16.093
Repositorio Institucional de la Universidad de Burgos
bubrep@ubu.es
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