Pato, Mauricio Porto. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access XVII, 178 p. 58 illus., 49 illus. in color. online resource. 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. 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. by Mauricio Porto Pato. Mathematical physics Algebras, Linear Probabilities System theory Nuclear physics Mathematical Physics Linear Algebra Probability Theory Complex Systems Nuclear Physics QC19.2-20.85 9783031602948 https://doi.org/10.1007/978-3-031-60294-8 https://doi.org/10.1007/978-3-031-60294-8 240621 20251030112323.0 978-3-031-60294-8