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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| Kieli: | englanti |
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Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
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| Painos: | 1st ed. 2024. |
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| Linkit: | https://doi.org/10.1007/978-3-031-60294-8 |
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| 100 | 1 | |a Pato, Mauricio Porto. |e author. |0 (orcid)0000-0003-2048-2089 |1 https://orcid.org/0000-0003-2048-2089 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Pseudo-Hermitian Random Matrices |h [electronic resource] / |c by Mauricio Porto Pato. |
| 250 | |a 1st ed. 2024. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2024. | |
| 300 | |a XVII, 178 p. 58 illus., 49 illus. in color. |b online resource. | ||
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| 505 | 0 | |a Chapter 1 Introduction -- Chapter 2 The pseudo-Hermitian condition -- Chapter 3 Pseudo-Hermitian b-Hermite ensemble with real eigenvalues1 -- Chapter 4 Pseudo-Hermitian -Hermite ensemble with an unbound metric2 -- Chapter 5 Pseudo-Hermitian -Hermite ensemble with an unbound metric -- Chapter 6 Pseudo-Hermitian b-Laguerre ensemble with real eigenvalues3 -- Chapter 7 Pseudo-Hermitian b-Laguerre ensemble with unbound metric -- Chapter 8 Pseudo-Hermitian -Laguerre ensemble with non-positive metric -- Chapter 9 The pseudo-Hermitian -Jacobi ensemble4 -- Chapter 10 Pseudo-Hermitian Gaussian matrices5 -- Chapter 11 Pseudo-Hermitian anti-Hermitian Gaussian matrices6 -- Chapter 12 Average characteristic polynomials7 -- Chapter 13 Spectral properties of pseudo-Hermitian matrices8 -- Chapter 14 Eigenvalues as quasi-particles -- Chapter 15 Entanglement of pseudo-Hermitian random states9. | |
| 520 | |a 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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| 532 | 8 | |a No reading system accessibility options actively disabled | |
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| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Algebras, Linear. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 0 | |a System theory. | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-60294-8 |
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