2003/07/31 by Stjepan Meljanac, S. Meljanac, Marijan Mileković +3 · 6 citations
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Degeneracy (biology) #Degenerate energy levels #Eigenvalues and eigenvectors #Energy spectrum #Excited state #Fock space #Ground state #Hamiltonian (control theory) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Theoretical physics #cond-mat.stat-mech #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1016/j.physletb.2003.08.029
published as Phys.Lett.B573:202-208,2003 · 16 pages, no figures, LateX, enlarged version that appeared in Phys.Lett.B
openalex publication_date 2003/10/01 · arxiv created 2004/05/14 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Using an algebraic approach (Fock space analysis), we construct ladder operators and find infinitely many, but not all, exact eigenstates of the model Hamiltonian. Besides the ground state energy, we deduce energies of the excited states. It turns out that the spectrum is linear in quantum numbers and that the higher-energy levels are degenerate. The dynamical symmetry responsible for degeneracy is SU(2). We also find the universal critical point at which the model exhibits singular behaviour. Finally, we make contact with some special cases mentioned in the literature.