03907nam a22005655i 4500 978-3-031-60294-8 DE-He213 20251030112323.0 cr nn 008mamaa 240621s2024 sz | s |||| 0|eng d 9783031602948 978-3-031-60294-8 10.1007/978-3-031-60294-8 doi QC19.2-20.85 PHU bicssc SCI040000 bisacsh PHU thema Pato, Mauricio Porto. author. aut http://id.loc.gov/vocabulary/relators/aut 79067 Pseudo-Hermitian Random Matrices [electronic resource] / by Mauricio Porto Pato. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XVII, 178 p. 58 illus., 49 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Chapter 1 Introduction -- Chapter 2 The pseudo-Hermitian condition -- Chapter 3 Pseudo-Hermitian b-Hermite ensemble with real eigenvalues1 -- Chapter 4 Pseudo-Hermitian 𝜷-Hermite ensemble with an unbound metric2 -- Chapter 5 Pseudo-Hermitian 𝜷-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 𝜷-Laguerre ensemble with non-positive metric -- Chapter 9 The pseudo-Hermitian 𝜷-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. 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. Mathematical physics. Algebras, Linear. 71217 Probabilities. 65724 System theory. 66519 Nuclear physics. Mathematical Physics. Linear Algebra. 71220 Probability Theory. 67428 Complex Systems. 66520 Nuclear Physics. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031602931 Printed edition: 9783031602955 Printed edition: 9783031602962 https://doi.org/10.1007/978-3-031-60294-8 ZDB-2-PHA ZDB-2-SXP 60894 60894