Work

Degenerate eigenvalues for Hamiltonians with no obvious symmetries

Year: 2005

Type: article

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 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.

Source: Advances in Theoretical and Mathematical Physics

DOI: 10.4310/atmp.2005.v9.n4.a4

Authors: Robert K. Bradley, Steven S. Gubser

Institution: Princeton University

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze

Funders: U.S. Department of Energy, Alfred P. Sloan Foundation

Awards: A SILICON-DRIFT-CHAMBER, A PARALLEL COMPUTER FORM, & READOUTDEVELOPMENT FOR AN ELECTROMAGNETIC CALORIMETER FOR THE SSC., G222768804, HIGH ENERGY PHYSICS RESEARCH