Pseudo-Hermitian Random Matrices (eBook)

Mauricio Porto Pato (Autor)

eBook Download: PDF

2024
178 Seiten
Springer Nature Switzerland (Verlag)
9783031602948 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 20.6.2024
• Zusatzinfo: XVII, 178 p. 58 illus., 49 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Schlagworte: 2 beta-Dyson index • absorption spectra • Beta-ensemble • Beta-Laguerre ensemble • Eigenvector delocalization • Emission spectra • Pseudo-Hermitian beta-ensemble • Pseudo-Hermiticity • symmetry breaking • Wishart model
• ISBN-13: 9783031602948 / 9783031602948