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 , one such Hamiltonian helps explain resonances in the spin relaxation rate of optically pumped Rb2, 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.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)