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August 2005 Degenerate eigenvalues for Hamiltonians with no obvious symmetries
Robert K. Bradley, Steven S. Gubser
Adv. Theor. Math. Phys. 9(4): 593-602 (August 2005).

Abstract

Certain Hamiltonians, based on two coupled quantum mechanical\break 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 [3], one such Hamiltonian helps explain resonances in the spin relaxation rate of optically pumped ${\rm Rb}_2$, 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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Robert K. Bradley. Steven S. Gubser. "Degenerate eigenvalues for Hamiltonians with no obvious symmetries." Adv. Theor. Math. Phys. 9 (4) 593 - 602, August 2005.

Information

Published: August 2005
First available in Project Euclid: 3 April 2006

zbMATH: 1121.81048
MathSciNet: MR2201107

Rights: Copyright © 2005 International Press of Boston

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Vol.9 • No. 4 • August 2005
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