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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.15768 |
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| _version_ | 1866916037606244352 |
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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 |
| id |
arxiv_https___arxiv_org_abs_2603_15768 |
| 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 |