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Main Author: Brandão, Paulo A.
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.15768
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author Brandão, Paulo A.
author_facet Brandão, Paulo A.
contents We study a minimal non-Hermitian trimer with latent symmetry formed by a cospectral pair of sites embedded in a three-site network with nonreciprocal couplings. We show that cospectrality provides a structural latent-symmetry constraint, whereas exact dark-state decoupling requires an additional algebraic matching condition among the couplings. For a dark-state-compatible representative of this cospectral class, the model admits an exact decomposition into dark and bright sectors: the dark mode is spectrally isolated and retains a complex eigenvalue, while the bright sector reduces to an effective non-Hermitian dimer. For a suitable choice of parameters, this reduced subsystem becomes $\mathcal{PT}$-symmetric and exhibits partial spectral reality, with two real eigenvalues coexisting with the complex dark eigenvalue. At the critical point, the bright sector hosts an embedded second-order exceptional point, which renders the full trimer defective and gives rise to the characteristic Jordan-block dynamics. These results establish the non-Hermitian trimer as a minimal analytically solvable setting in which latent symmetry, sector-resolved $\mathcal{PT}$ symmetry, and exceptional-point physics naturally coexist.
format Preprint
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institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Latent symmetry in a minimal non-Hermitian trimer
Brandão, Paulo A.
Quantum Physics
We study a minimal non-Hermitian trimer with latent symmetry formed by a cospectral pair of sites embedded in a three-site network with nonreciprocal couplings. We show that cospectrality provides a structural latent-symmetry constraint, whereas exact dark-state decoupling requires an additional algebraic matching condition among the couplings. For a dark-state-compatible representative of this cospectral class, the model admits an exact decomposition into dark and bright sectors: the dark mode is spectrally isolated and retains a complex eigenvalue, while the bright sector reduces to an effective non-Hermitian dimer. For a suitable choice of parameters, this reduced subsystem becomes $\mathcal{PT}$-symmetric and exhibits partial spectral reality, with two real eigenvalues coexisting with the complex dark eigenvalue. At the critical point, the bright sector hosts an embedded second-order exceptional point, which renders the full trimer defective and gives rise to the characteristic Jordan-block dynamics. These results establish the non-Hermitian trimer as a minimal analytically solvable setting in which latent symmetry, sector-resolved $\mathcal{PT}$ symmetry, and exceptional-point physics naturally coexist.
title Latent symmetry in a minimal non-Hermitian trimer
topic Quantum Physics
url https://arxiv.org/abs/2603.15768