Abstract
Pseudo-Hermitian and PT-symmetric matrices have been a topic of interest since the first papers on the subject in the late 90s. In this paper we utilize properties of tridiagonal random matrices described in the framework of generalized \(\beta \) ensembles to explore variations of that ensemble, which cause the eigenvalues to move from the real line into the complex plane in conjugate pairs, while still maintaining the pseudo-Hermitian property.
Keywords
- Classical Gaussian Ensembles
- Quasi-hermitian Operators
- Characteristic polynomialCharacteristic Polynomial
- Pseudo Hermitian
- Fixed Matrix Size
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Acknowledgments
Fruitful discussions with E.J.V. de Passos and N. Hatano are acknowledged. G.M. is supported by the Brazilian CNPq agency and M.P.P. is supported by the Brazilian CNPq and FAPESP agencies.
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Marinello, G., Pato, M.P. (2016). Pseudo-Hermitian \(\beta \)-Ensembles with Complex Eigenvalues. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_20
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DOI: https://doi.org/10.1007/978-3-319-31356-6_20
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