2016/05/06 by O. Cherbal, D. Trifonov, M. Zenad
Mathematics · Physics and Astronomy · #Annihilation #Creation and annihilation operators #Degeneracy (biology) #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Hermitian matrix #Homogeneous space #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/s10773-016-3151-3
15 pages
arxiv created 2016/05/06 · openalex created_date 2016/06/24 · openalex publication_date 2016/09/13 · arxiv updated 2016/10/12 · openalex updated_date 2026/08/05
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue degeneracy can be represented in the oscillator-like form in terms of pseudofermionic creation and annihilation operators for both real and complex eigenvalues. The example of most general four-level traceless Hamiltonian with odd time-reversal symmetry, which is an extension of the SO(5) Hermitian Hamiltonian, is considered in greater and explicit detail.