Complex Eigenvalues in a pseudo-Hermitian \b{eta}-Laguerre ensemble
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914152872673280 |
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| author | Goulart, Cleverson Andrade Oshanin, Gleb Pato, Mauricio Porto |
| author_facet | Goulart, Cleverson Andrade Oshanin, Gleb Pato, Mauricio Porto |
| contents | Non-Hermitian PT-symmetric models have been extensively studied in recent years. Following the seminal work that reduced classical random matrix ensembles to a tridiagonal form, several efforts have aimed to generalize this framework to non-Hermitian extensions of the so-called \b{eta}-ensembles. In particular, while the transition of eigenvalues from the real axis to the complex plane has been well characterized for the \b{eta}-Hermite ensemble under symmetry breaking, the behavior of the \b{eta}-Laguerre ensemble in a similar non-Hermitian setting remains
less understood. In this work, we investigate an ensemble of unstable matrices isospectral to the \b{eta}-Laguerre ensemble. Introducing a small non-Hermitian perturbation breaks the symmetry and drives the eigenvalues into the complex plane. We derive analytical expressions for the loci of complex-conjugate eigenvalue pairs, which organize into a balloon-like structure in the complex plane, followed by a discrete finite line of real eigenvalues. The asymptotic behavior of these eigenvalues is analyzed in the large matrix-size limit, and our theoretical predictions are supported by numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complex Eigenvalues in a pseudo-Hermitian \b{eta}-Laguerre ensemble Goulart, Cleverson Andrade Oshanin, Gleb Pato, Mauricio Porto Statistical Mechanics Mathematical Physics Quantum Physics Non-Hermitian PT-symmetric models have been extensively studied in recent years. Following the seminal work that reduced classical random matrix ensembles to a tridiagonal form, several efforts have aimed to generalize this framework to non-Hermitian extensions of the so-called \b{eta}-ensembles. In particular, while the transition of eigenvalues from the real axis to the complex plane has been well characterized for the \b{eta}-Hermite ensemble under symmetry breaking, the behavior of the \b{eta}-Laguerre ensemble in a similar non-Hermitian setting remains less understood. In this work, we investigate an ensemble of unstable matrices isospectral to the \b{eta}-Laguerre ensemble. Introducing a small non-Hermitian perturbation breaks the symmetry and drives the eigenvalues into the complex plane. We derive analytical expressions for the loci of complex-conjugate eigenvalue pairs, which organize into a balloon-like structure in the complex plane, followed by a discrete finite line of real eigenvalues. The asymptotic behavior of these eigenvalues is analyzed in the large matrix-size limit, and our theoretical predictions are supported by numerical simulations. |
| title | Complex Eigenvalues in a pseudo-Hermitian \b{eta}-Laguerre ensemble |
| topic | Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2511.08857 |