Maximal couplings in -symmetric chain models with the real spectrum of energies

2007/03/23 by Miloslav Znojil · 4 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:13P10 #msc:14J81 #msc:14M12 #msc:46C20 #msc:47B50 #msc:81Q10

paper · pdf · doi:10.1088/1751-8113/40/18/012

published as J. Phys. A: Math. Theor. 40 (2007) 4863-4875 · 18 pp., 2 figs

arxiv created 2007/03/23 · openalex publication_date 2007/04/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

The domain of all the coupling strengths compatible with the reality of the energies is studied for a family of non-Hermitian N × N matrix Hamiltonians H ( N ) with tridiagonal and -symmetric structure. At all dimensions N , the coordinates are found of the extremal points at which the boundary hypersurface touches the circumscribed sphere (for odd N = 2 M + 1) or ellipsoid (for even N = 2 K ).

Cited by

• Discrete quantum square well of the first kind
• Decays of degeneracies in -symmetric ring-shaped lattices
• Unitarity corridors to exceptional points
• Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices