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

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

2007-03-23

arxiv.org/abs/math-ph/0703070v1

J. Phys. A: Math. Theor. 40 (2007) 4863-4875

Physics

Mathematical Physics

18 pp., 2 figs

Scientific paper

10.1088/1751-8113/40/18/012

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

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