title: Detecting level crossings without looking at the spectrum.
abstract: 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.
authors.affiliation: School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
authors.forename: M
authors.initials: M
authors.lastname: Bhattacharya
authors.forename: C
authors.initials: C
authors.lastname: Raman