RT info:eu-repo/semantics/article
T1 Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature
A1 Ballesteros Castañeda, Ángel
A1 Gutiérrez Sagredo, Iván
K1 Shannon entropy
K1 Quantum information
K1 Nonlinear oscillator
K1 Non-constant curvature
K1 Darboux III space
K1 Física
K1 Physics
K1 Matemáticas
K1 Mathematics
AB The so-called Darboux III oscillator is an exactly solvable N-dimensional nonlinear oscillator definedon a radially symmetric space with non-constant negative curvature. This oscillator can be interpretedas a smooth (super)integrable deformation of the usual N-dimensional harmonic oscillator in terms ofa non-negative parameter λ which is directly related to the curvature of the underlying space. In thispaper, a detailed study of the Shannon information entropy for the quantum version of the DarbouxIII 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 recoveredin the limit of vanishing curvature λ → 0. However, the Fourier transform of the Darboux III wavefunctions cannot be computed in exact form, thus preventing the analytical study of the informationentropy in momentum space. Nevertheless, we have computed the latter numerically both in the oneand three-dimensional cases and we have found that by increasing the absolute value of the negativecurvature (through a larger λ parameter) the information entropy in position space increases, while inmomentum space it becomes smaller. This result is indeed consistent with the spreading propertiesof the wave functions of this quantum nonlinear oscillator, which are explicitly shown. The sum ofthe entropies in position and momentum spaces has been also analysed in terms of the curvature: forall excited states such total entropy decreases with λ, but for the ground state the total entropy isminimized when λ vanishes, and the corresponding uncertainty relation is always fulfilled.
PB Elsevier
SN 0167-2789
YR 2023
FD 2023-03
LK http://hdl.handle.net/10259/7471
UL http://hdl.handle.net/10259/7471
LA eng
NO 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.
DS Repositorio Institucional de la Universidad de Burgos
RD 06-may-2024