arXiv subjects

Ignacio Baena-Jimenez

Publications and source records attributed to Ignacio Baena-Jimenez.

2 recordsLinked to original sources

arXiv2026

The Fock-Darwin-Darboux system: eigenstates, information entropies and dispersion-like measures

The Fock-Darwin (FD) quantum system describes the motion on the plane of a charged particle under the action of an isotropic oscillator potential together with a perpendicular constant magnetic field. When the isotropic oscillator is suppressed, the FD system leads to the Landau Hamiltonian with infinitely degenerate Landau levels. The Fock-Darwin-Darboux (FDD) system is the generalisation of the FD system to a particle moving on the Darboux III space, which is a conformally flat surface with non-constant negative curvature. We present a systematic study of some information-theoretic entropy and dispersion-like measures for these quantum systems. Since both systems are exactly solvable, analytical expressions for Shannon, Rényi and Tsallis entropies, among others, can be obtained. We show that for the FD system, its information-theoretic measures are formally the same as the ones for the harmonic oscillator, provided a modified effective frequency depending on the magnetic field is introduced. In the FDD case, the nonlinear nature of the underlying manifold precludes the existence of a simple closed form for the wave-function on momentum space, which is numerically analysed. We compare the numerical behaviour of the different entropy measures and we analyse the interplay arising in the FDD system between the curvature parameter and the magnetic field. In particular, it is shown that the Landau system on the Darboux III space has no infinitely degenerate Landau levels.

quant-ph↗

arXiv2025

Rényi and Tsallis information entropies for the Darboux III quantum nonlinear oscillator

The Darboux III oscillator is an exactly solvable $N$-dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. Its one-dimensional version can be seen as a position dependent mass system whose mass function $μ= (1 + λx^2)$ depends on the nonlinearity parameter $λ$, such that in the limit $λ\to 0$ the harmonic oscillator is recovered. In this paper, a detailed study of the entropic moments and of the Rényi and Tsallis information entropies for the quantum version of the one-dimensional Darboux III oscillator is presented. In particular, analytical expressions for the aforementioned quantities in position space are obtained. Since the Fourier transform of the Darboux III wave functions does not admit a closed form expression, a numerical analysis of these quantities has been performed. Throughout the paper the interplay between the entropy parameter $α$ and the nonlinearity parameter $λ$ is analysed, and known results for the Shannon entropy of the Darboux III and for the Rényi and Tsallis entropies of the harmonic oscillator are recovered in the limits $α\to 1$ and $λ\to 0$, respectively. Finally, motivated by the strong non-linear effects arising when large values of $λ$ and/or highly excited states are considered, an approximation to the probability density function valid in those regimes is presented. From it, an analytical approximation to the probability density in momentum space can be obtained, and some of the previously observed effects arising from the interplay between $α$ and $λ$ can be explained.

quant-ph↗