MOMENTAN AUSVERKAUFT
Über dieses Produkt
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-101470419130
ISBN-139781470419134
eBay Product ID (ePID)219177989
Product Key Features
Number of Pages320 Pages
LanguageEnglish
Publication NameRandom Operators : Disorder Effects on Quantum Spectra and Dynamics
Publication Year2015
SubjectPhysics / Quantum Theory, Functional Analysis, Probability & Statistics / Stochastic Processes
TypeTextbook
AuthorSimone Warzel, Michael Aizenman
Subject AreaMathematics, Science
SeriesGraduate Studies in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.9 in
Item Weight26.5 Oz
Item Length10.2 in
Item Width7.3 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2015-025474
ReviewsIt has been almost 25 years since the last major book on this subject. The authors masterfully update the subject but more importantly present their own probabilistic insights in clear fashion. This wonderful book is ideal for both researchers and advanced students. - Barry Simon, California Institute of Technology
Dewey Edition23
Series Volume Number168
IllustratedYes
Volume NumberVol. 168
Dewey Decimal535/.150151923
Table Of ContentIntroduction General relations between spectra and dynamics Ergodic operators and their self-averaging properties Density of states bounds: Wegner estimate and Lifshitz tails The relation of Green functions to eigenfunctions Anderson localization through path expansions Dynamical localization and fractional moment criteria Fractional moments from an analytical perspective Strategies for mapping exponential decay Localization at high disorder and at extreme energies Constructive criteria for Anderson localization Complete localization in one dimension Diffusion hypothesis and the Green-Kubo-Streda formula Integer quantum Hall effect Resonant delocalization Phase diagrams for regular tree graphs The eigenvalue point process and a conjectured dichotomy Elements of spectral theory Herglotz-Pick functions and their spectra Bibliography Index
SynopsisProvides 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., 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.
LC Classification NumberQA274.28.A39 2015
