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

Miloslav Znojil
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Abstract

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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Miloslav Znojil. 2007-03-23. Maximal couplings in PT-symmetric chain-models with the real spectrum of energies. https://doi.org/10.1088/1751-8113/40/18/012

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