Gravitación y Física Matemática

The Darboux III oscillator: curvature. integrability and information entropy

by Prof. Ángel Ballesteros Castañeda (Universidad de Burgos)


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 which is directly related to the curvature of the underlying space. In this seminar, the integrability properties of the Darboux III oscillator are reviewed, 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.