Degenerate eigenvalues for Hamiltonians with no obvious symmetries

Steven S. Gubser, Robert K. Bradley

Research output: Contribution to journalArticle

2 Scopus citations

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 [3], 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.

Original languageEnglish (US)
Pages (from-to)593-602
Number of pages10
JournalAdvances in Theoretical and Mathematical Physics
Volume9
Issue number4
DOIs
StatePublished - Aug 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

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