2006/04/30 by M. Bhattacharya, C. Raman, Chandra Raman · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #physics.atom-ph
paper · pdf · doi:10.1103/physrevlett.97.140405
4 pages, new title, no figures, accepted by Phys. Rev. Lett
arxiv created 2006/09/14 · openalex publication_date 2006/10/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In many physical systems it is important to be aware of the crossings and avoided crossings which occur when eigenvalues of a physical observable are varied using an external parameter. We have discovered a powerful algebraic method of finding such crossings via a mapping to the problem of locating the roots of a polynomial in that parameter. We demonstrate our method on atoms and molecules in a magnetic field, where it has implications in the search for Feshbach resonances. In the atomic case our method allows us to point out a new class of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. In the case of molecules, it enables us to find curve crossings with practically no knowledge of the corresponding Born-Oppenheimer potentials.