Pseudo-Hermitian Random Matrices [E-Book] /

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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Pato, Mauricio Porto, author
1st edition 2024.
Cham : Springer, 2024
XVII, 178 pages 58 illustrations, 49 illustrations in color (online resource)
englisch
9783031602948
10.1007/978-3-031-60294-8
Algebras, Linear.
Mathematical physics.
Nuclear physics.
Probabilities.
System theory.


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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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650 0 |a Nuclear physics. 
650 0 |a Probabilities. 
650 0 |a System theory. 
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