Random Operators - Disorder Effects on Quantum Spectra and Dynamics (Hardcover)

This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization-presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Graduate Studies in Mathematics
Release date:	December 2015
Authors:	Michael Aizenman • Simone Warzel
Dimensions:	254 x 178mm (L x W)
Format:	Hardcover
Pages:	320
ISBN-13:	978-1-4704-1913-4
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > General Books > Science & Mathematics > Mathematics > Applied mathematics > General Promotions
LSN:	1-4704-1913-0
Barcode:	9781470419134

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