Del i serien Graduate Studies in Mathematics

Random Operators

Disorder Effects on Quantum Spectra and Dynamics

Inbunden, Engelska, 2015

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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

Utgivningsdatum2015-12-30
Mått178 x 254 x undefined mm
Vikt755 g
FormatInbunden
SpråkEngelska
SerieGraduate Studies in Mathematics
Antal sidor320
FörlagAmerican Mathematical Society
ISBN9781470419134

Tillhör följande kategorier

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