dorsal/arxiv
View SchemaDegenerate eigenvalues for Hamiltonians with no obvious symmetries
| Authors | Steven S. Gubser, Robert K. Bradley |
|---|---|
| Categories | |
| ArXiv ID | physics/0312118 |
| URL | https://arxiv.org/abs/physics/0312118 |
| Journal | Adv.Theor.Math.Phys. 9 (2005) 593-602 |
Abstract
Certain Hamiltonians based on two coupled quantum mechanical spins exhibit degenerate eigenvalues despite having no obvious non-abelian symmetries. Operators acting to permute the degenerate states do not have a simple form when expressed as polynomials of the generators of rotations for the respective spins. As observed in [1], one such Hamiltonian helps explain resonances in the spin relaxation rate of optically pumped Rb_2, as a function of applied magnetic field. We give an explanation of why the degeneracies exist, based on properties of the commutator and anti-commutator of the Hamiltonian and its image under magnetic field reversal.
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"abstract": "Certain Hamiltonians based on two coupled quantum mechanical spins exhibit\ndegenerate eigenvalues despite having no obvious non-abelian symmetries.\nOperators acting to permute the degenerate states do not have a simple form\nwhen expressed as polynomials of the generators of rotations for the respective\nspins. As observed in [1], one such Hamiltonian helps explain resonances in the\nspin relaxation rate of optically pumped Rb_2, as a function of applied\nmagnetic field. We give an explanation of why the degeneracies exist, based on\nproperties of the commutator and anti-commutator of the Hamiltonian and its\nimage under magnetic field reversal.",
"arxiv_id": "physics/0312118",
"authors": [
"Steven S. Gubser",
"Robert K. Bradley"
],
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"physics.atom-ph"
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"journal_ref": "Adv.Theor.Math.Phys. 9 (2005) 593-602",
"title": "Degenerate eigenvalues for Hamiltonians with no obvious symmetries",
"url": "https://arxiv.org/abs/physics/0312118"
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