{"title":"A quadrupole oscillator as an integrable model","authors":"","doi":"10.1016/j.physleta.2024.130032","DOIUrl":null,"url":null,"abstract":"<div><div>A quadrupole oscillator is presented as an integrable model in the Born-Oppenheimer formalism with an electronic Hamiltonian being the quadrupole tensor. The electronic states of present concern are associated with a doubly degenerate positive eigenvalue of the electronic Hamiltonian, and accordingly the nuclear Hamiltonian takes a <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> matrix form. While the potential function for nuclear motion is proportional to <span><math><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, the kinetic energy operator is rather complicated, containing coupling terms with a Berry connection through adiabatic approximation. The energy eigenvalues, which receive a modification by a Chern number, get closer to those for the 3D isotropic harmonic oscillator if the angular momentum quantum number becomes sufficiently large.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375960124007266","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
A quadrupole oscillator is presented as an integrable model in the Born-Oppenheimer formalism with an electronic Hamiltonian being the quadrupole tensor. The electronic states of present concern are associated with a doubly degenerate positive eigenvalue of the electronic Hamiltonian, and accordingly the nuclear Hamiltonian takes a matrix form. While the potential function for nuclear motion is proportional to , the kinetic energy operator is rather complicated, containing coupling terms with a Berry connection through adiabatic approximation. The energy eigenvalues, which receive a modification by a Chern number, get closer to those for the 3D isotropic harmonic oscillator if the angular momentum quantum number becomes sufficiently large.
期刊介绍:
Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.