dorsal/arxiv
View SchemaDetecting level crossings without looking at the spectrum
| Authors | M. Bhattacharya, C. Raman |
|---|---|
| Categories | |
| ArXiv ID | physics/0604213 |
| URL | https://arxiv.org/abs/physics/0604213 |
| DOI | 10.1103/PhysRevLett.97.140405 |
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.
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"abstract": "In many physical systems it is important to be aware of the crossings and\navoided crossings which occur when eigenvalues of a physical observable are\nvaried using an external parameter. We have discovered a powerful algebraic\nmethod of finding such crossings via a mapping to the problem of locating the\nroots of a polynomial in that parameter. We demonstrate our method on atoms and\nmolecules in a magnetic field, where it has implications in the search for\nFeshbach resonances. In the atomic case our method allows us to point out a new\nclass of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. In the\ncase of molecules, it enables us to find curve crossings with practically no\nknowledge of the corresponding Born-Oppenheimer potentials.",
"arxiv_id": "physics/0604213",
"authors": [
"M. Bhattacharya",
"C. Raman"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevLett.97.140405",
"title": "Detecting level crossings without looking at the spectrum",
"url": "https://arxiv.org/abs/physics/0604213"
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