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arXiv · 1909.02035

Unitarity corridors to exceptional points

Miloslav Znojil
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Abstract

Non-Hermitian quantum one-parametric $N$ by $N$ matrix Hamiltonians $H^{(N)}(λ)$ with real spectra are considered. Their special choice $H^{(N)}(λ)=J^{(N)}+λ\,V^{(N)}(λ)$ is studied at small $λ$, with a general $N^2-$parametric real-matrix perturbation $λ\,V^{(N)}(λ)$, and with the exceptional-point-related "unperturbed" Jordan-block Hamiltonian $J^{(N)}$. A "stability corridor" ${\cal S}$ of the parameters $λ$ is then sought guaranteeing the reality of spectrum and realizing a unitary-system-evolution access to the exceptional-point boundary of stability. The corridors are then shown $N-$dependent and "narrow", corresponding to certain specific, unitarity-compatible perturbations with "admissible" matrix elements $V^{(N)}_{j+k,j}(λ) ={\cal O}(λ^{(k-1)/2})\,$ at subscripts $k=1,2,\ldots,N-1\,$ and at all $j$.

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Miloslav Znojil. 2019-09-04. Unitarity corridors to exceptional points. https://doi.org/10.1103/physreva.100.032124

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