Classical and quantum integrability of the three-dimensional generalized trapped ion Hamiltonian

Idriss El Fakkousy, Bouchta Zouhairi, Mohammed Benmalek, Jaouad Kharbach, Abdellah Rezzouk and Mohammed Ouazzani-Jamil

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

Abstract: In this paper, we study the trapped ion Hamiltonian in three-dimensional (3D) with the generalized potential in the quadrupole field with superposition of the hexapole and octopole fields. We determine new integrable cases by using the Painlevé analysis and find the second and third classical invariants for each P-case. Moreover, we perturb this Hamiltonian by an inverse square potential and we prove that the 3D perturbed Hamiltonian is completely integrable in the sense of Liouville for the special conditions. Quantum invariants are obtained by adding deformation terms, computed using Moyal's bracket, to the corresponding classical counterparts. Furthermore, we use python programming language to plot the third classical invariant, the deformation and the third quantum invariant in phase space for each quantum integrable case in order to confirm the analytical results.

Keywords: Painlevé analysis; Dynamic system; Hamiltonian system; Trapped ion; Three-dimensional integrability; Classical and quantum integrability (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922005719
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005719

DOI: 10.1016/j.chaos.2022.112361

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().