Random Operators: Disorder Effects on Quantum Spectra and Dynamics 1470419130, 978-1-4704-1913-4
This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topic
449 53 2MB
English Pages 326 [342] Year 2015
Table of contents :
Content: 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
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