Random Operators

Disorder Effects on Quantum Spectra and Dynamics

AvMichael Aizenman,Simone Warzel

Inbunden, Engelska, 2015

Del i serien Graduate Studies in Mathematics

1 518 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2015-12-30
Mått:178 x 254 x undefined mm
Vikt:755 g
Format:Inbunden
Språk:Engelska
Serie:Graduate Studies in Mathematics
Antal sidor:320
Förlag:American Mathematical Society
ISBN:9781470419134

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Mer om författaren

Michael Aizenman, Princeton University, NJ, USA.Simone Warzel, Technische Universitat Munchen, Germany.

Recensioner i media

It 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

Innehållsförteckning

IntroductionGeneral relations between spectra and dynamicsErgodic operators and their self-averaging propertiesDensity of states bounds: Wegner estimate and Lifshitz tailsThe relation of Green functions to eigenfunctionsAnderson localization through path expansionsDynamical localization and fractional moment criteriaFractional moments from an analytical perspectiveStrategies for mapping exponential decayLocalization at high disorder and at extreme energiesConstructive criteria for Anderson localizationComplete localization in one dimensionDiffusion hypothesis and the Green-Kubo-Streda formulaInteger quantum Hall effectResonant delocalizationPhase diagrams for regular tree graphsThe eigenvalue point process and a conjectured dichotomyElements of spectral theoryHerglotz-Pick functions and their spectraBibliographyIndex