000 03907nam a22005655i 4500
001 978-3-031-60294-8
003 DE-He213
005 20251030112323.0
007 cr nn 008mamaa
008 240621s2024 sz | s |||| 0|eng d
020 _a9783031602948
_9978-3-031-60294-8
024 7 _a10.1007/978-3-031-60294-8
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
100 1 _aPato, Mauricio Porto.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_979067
245 1 0 _aPseudo-Hermitian Random Matrices
_h[electronic resource] /
_cby Mauricio Porto Pato.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXVII, 178 p. 58 illus., 49 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _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.
520 _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.
650 0 _aMathematical physics.
650 0 _aAlgebras, Linear.
_971217
650 0 _aProbabilities.
_965724
650 0 _aSystem theory.
_966519
650 0 _aNuclear physics.
650 1 4 _aMathematical Physics.
650 2 4 _aLinear Algebra.
_971220
650 2 4 _aProbability Theory.
_967428
650 2 4 _aComplex Systems.
_966520
650 2 4 _aNuclear Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031602931
776 0 8 _iPrinted edition:
_z9783031602955
776 0 8 _iPrinted edition:
_z9783031602962
856 4 0 _uhttps://doi.org/10.1007/978-3-031-60294-8
912 _aZDB-2-PHA
912 _aZDB-2-SXP
999 _c60894
_d60894