The Fock-Darwin-Darboux system: geometry, integrability, eigenstates and quantum information measures

Speaker:  Iván Gutiérrez Sagredo (UBU)
Date:  Thursday, 30 April 2026 - 12:00
Place:  Aula Gris 3, ICMAT
Online:  Zoom. ID: 810 9248 3225; Código acceso: 183643

Abstract:

In this talk we will present the so-called Darboux III oscillator, which 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 related to the curvature of the underlying space. In particular, when N=2, the Darboux III quantum oscillator can be coupled to a magnetic field, giving rise to a very interesting multi-parametric system, denoted as the Fock-Darwin-Darboux (FDD) system and containing the Darboux III, the Fock-Darwin, the Landau and the harmonic oscillator systems as particular examples. Exploiting the exact solvability of the system, we will be able to obtain explicit expressions for its spectrum and eigenfunctions, and to obtain exact expressions for the Shannon, Rényi and Tsallis entropies and position and momentum expected values. Also, we will discuss the interplay between the curvature, oscillator and magnetic field parameters.
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