Pseudo-Hermitian Random Matrices [E-Book] / by Mauricio Porto Pato.
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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Full text |
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| Personal Name(s): | Pato, Mauricio Porto, author |
| Edition: |
1st edition 2024. |
| Imprint: |
Cham :
Springer,
2024
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| Physical Description: |
XVII, 178 pages 58 illustrations, 49 illustrations in color (online resource) |
| Note: |
englisch |
| ISBN: |
9783031602948 |
| DOI: |
10.1007/978-3-031-60294-8 |
| Subject (LOC): |
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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. |