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    Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10259/7471

    Título
    Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature
    Autor
    Ballesteros Castañeda, ÁngelAutoridad UBU Orcid
    Gutiérrez Sagredo, IvánAutoridad UBU Orcid
    Publicado en
    Physica D: Nonlinear Phenomena. 2023, V. 445, 133618
    Editorial
    Elsevier
    Fecha de publicación
    2023-03
    ISSN
    0167-2789
    DOI
    10.1016/j.physd.2022.133618
    Résumé
    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.
    Palabras clave
    Shannon entropy
    Quantum information
    Nonlinear oscillator
    Non-constant curvature
    Darboux III space
    Materia
    Física
    Physics
    Matemáticas
    Mathematics
    URI
    http://hdl.handle.net/10259/7471
    Versión del editor
    https://doi.org/10.1016/j.physd.2022.133618
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    • Artículos FISMAT-UBU
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    Ballesteros-pd_2023.pdf
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