Detecting level crossings without looking at the spectrum

Details Detecting level crossings without looking at the spectrum Detecting level crossings without looking at the spectrum

2006-04-26

arxiv.org/abs/physics/0604213v2

Physics

Atomic Physics

4 pages, new title, no figures, accepted by Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.97.140405

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.

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