Pseudo-Hermitian Random Matrices
This book is a comprehensive guide to pseudo-Hermitian random matrices, their properties, and their role in many models that are relevant to physical processes. The book starts by showing how the concept of pseudo-Hermiticity emerged from studies of PT-symmetric systems which aroused the interest of...
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| Format: | Électronique eBook |
| Langue: | anglais |
| Publié: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
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| Édition: | 1st ed. 2024. |
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| Accès en ligne: | https://doi.org/10.1007/978-3-031-60294-8 |
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| Résumé: | This book is a comprehensive guide to pseudo-Hermitian random matrices, their properties, and their role in many models that are relevant to physical processes. The book starts by showing how the concept of pseudo-Hermiticity emerged from studies of PT-symmetric systems which aroused the interest of the random matrix theory community. The chapters that follow discuss the consequences of the pseudo-Hermitian condition to the eigen-decomposition of non-Hermitian matrices, and an investigation of pseudo-Hermitian random matrices in tridiagonal form, discussing the scenario with real eigenvalues, and the appearance of complex eigenvalues generated by unbound and non-positive metrics. Subsequently, the author introduces pseudo-Hermitian Gaussian matrices and their properties including characteristic polynomials, and statistical properties of their eigenvalues. Finally, in the last chapter, the time invariance of the metric is upended and a pseudo-Hermitian model with a time dependent metricis constructed to discuss the time evolution of entangled states. |
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| Description matérielle: | XVII, 178 p. 58 illus., 49 illus. in color. online resource. |
| ISBN: | 9783031602948 |
| DOI: | 10.1007/978-3-031-60294-8 |