Horizons of stability in matrix Hamiltonians

TL;DR

This paper identifies specific classes of non-Hermitian matrix Hamiltonians with real spectra, providing explicit formulas for their stability boundaries, which are crucial for understanding their physical observability.

Contribution

It introduces a class of pseudo-Hermitian matrix Hamiltonians with analytically defined stability horizons, advancing the understanding of their spectral properties.

Findings

Explicit formulas for stability boundaries of certain matrix Hamiltonians

Identification of pseudo-Hermitian Hamiltonians with real spectra

Enhanced understanding of spectral stability regions

Abstract

Non-Hermitian Hamiltonians H possess the real (i.e., observable) spectra inside certain specific domains of parameters D. In general, the determination of their observability-horizon boundaries is difficult. We list the pseudo-Hermitian real N by N matrix Hamiltonians for which the prototype horizons are defined by closed analytic formulae.