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Pseudo-hermitian random matrices

Record Type:	Electronic resources : Monograph/item
Title/Author:	Pseudo-hermitian random matrices/ by Mauricio Porto Pato.
Author:	Pato, Mauricio Porto.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	xvii, 178 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Chapter 1 Introduction -- Chapter 2 The pseudo-Hermitian condition -- Chapter 3 Pseudo-Hermitian b-Hermite ensemble with real eigenvalues1 -- Chapter 4 Pseudo-Hermitian {cedil}{9D}{9C}{hardsign}-Hermite ensemble with an unbound metric2 -- Chapter 5 Pseudo-Hermitian {cedil}{9D}{9C}{hardsign}-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 {cedil}{9D}{9C}{hardsign}-Laguerre ensemble with non-positive metric -- Chapter 9 The pseudo-Hermitian {cedil}{9D}{9C}{hardsign}-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.
Contained By:	Springer Nature eBook
Subject:	Random matrices. -
Online resource:	https://doi.org/10.1007/978-3-031-60294-8
ISBN:	9783031602948

Pseudo-hermitian random matrices
Pato, Mauricio Porto.

Pseudo-hermitian random matrices[electronic resource] /by Mauricio Porto Pato. - Cham :Springer Nature Switzerland :2024. - xvii, 178 p. :ill. (some col.), digital ;24 cm.

Chapter 1 Introduction -- Chapter 2 The pseudo-Hermitian condition -- Chapter 3 Pseudo-Hermitian b-Hermite ensemble with real eigenvalues1 -- Chapter 4 Pseudo-Hermitian {cedil}{9D}{9C}{hardsign}-Hermite ensemble with an unbound metric2 -- Chapter 5 Pseudo-Hermitian {cedil}{9D}{9C}{hardsign}-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 {cedil}{9D}{9C}{hardsign}-Laguerre ensemble with non-positive metric -- Chapter 9 The pseudo-Hermitian {cedil}{9D}{9C}{hardsign}-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.

ISBN: 9783031602948

Standard No.: 10.1007/978-3-031-60294-8doiSubjects--Topical Terms:

646309
Random matrices.

LC Class. No.: QA196.5 / .P38 2024

Dewey Class. No.: 512.9434

Pseudo-hermitian random matrices
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100 1 $a Pato, Mauricio Porto. $3 3719576
245 1 0 $a Pseudo-hermitian random matrices $h [electronic resource] / $c by Mauricio Porto Pato.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a xvii, 178 p. : $b ill. (some col.), digital ; $c 24 cm.
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 {cedil}{9D}{9C}{hardsign}-Hermite ensemble with an unbound metric2 -- Chapter 5 Pseudo-Hermitian {cedil}{9D}{9C}{hardsign}-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 {cedil}{9D}{9C}{hardsign}-Laguerre ensemble with non-positive metric -- Chapter 9 The pseudo-Hermitian {cedil}{9D}{9C}{hardsign}-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.
650 0 $a Random matrices. $3 646309
650 1 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Linear Algebra. $3 3338825
650 2 4 $a Probability Theory. $3 3538789
650 2 4 $a Complex Systems. $3 1566441
650 2 4 $a Nuclear Physics. $3 2017604
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-60294-8
950 $a Physics and Astronomy (SpringerNature-11651)