03701nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001700172072001600189072002300205072001500228100009000243245008700333250001800420264006900438300006600507336002600573337002600599338003600625347002400661505090800685520107001593650002602663650002902689650002602718650002602744650002102770650002602791650002702817650003102844650002802875650002102903710003402924773002602958776003602984776003603020776003603056856004603092912001403138912001403152999001703166978-3-031-60294-8DE-He21320251030112323.0cr nn 008mamaa240621s2024    sz |    s    |||| 0|eng d  a97830316029489978-3-031-60294-87 a10.1007/978-3-031-60294-82doi 4aQC19.2-20.85 7aPHU2bicssc 7aSCI0400002bisacsh 7aPHU2thema1 aPato, Mauricio Porto.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97906710aPseudo-Hermitian Random Matricesh[electronic resource] /cby Mauricio Porto Pato.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXVII, 178 p. 58 illus., 49 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aChapter 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.  aThis 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. 0aMathematical physics. 0aAlgebras, Linear.971217 0aProbabilities.965724 0aSystem theory.966519 0aNuclear physics.14aMathematical Physics.24aLinear Algebra.97122024aProbability Theory.96742824aComplex Systems.96652024aNuclear Physics.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303160293108iPrinted edition:z978303160295508iPrinted edition:z978303160296240uhttps://doi.org/10.1007/978-3-031-60294-8  aZDB-2-PHA  aZDB-2-SXP  c60894d60894