Caught by disorder bound states in random media Peter Stollmann

Contine bibliogr.si index

Machine generated contents note: 1 Getting Started 1 -- Prologue1 -- 1.1 Bound states versus extended states7 -- 1.2 Ergodic operator families11 -- 1.3 Some important examples18 -- 1.4 Our basic models (P+A) and (DIV)21 -- 1.5 Localization and Lifshitz tails: the heuristic picture31 -- 2 Analysis of Anderson-type Models 37 -- Prologue37 -- 2.1 Lifshitz tails for (P+A)39 -- 2.2 Initial length scale estimates44 -- 2.3 Wegner estimates48 -- 2.4 Combes-Thomas estimates54 -- 2.5 Changing cubes62 -- 3 Multiscale Analysis 69 -- Prologue 69 -- 3.1 Idea of the proof and historical notes71 -- 3.2 M ultiscale Analysis76 -- 3.3 Exponential localization90 -- 3.4 Dynamical localization98 -- 3.5 More models108 -- 4 Appendix 111 -- 4.1 A short story of selfadjoint operators111 -- 4.1.1 Welcome to Hilbert space111 -- 4.1.2 Selfadjoint operators and forms114 -- 4.1.3 Schrodinger operators116 -- 4.1.4 Spectra and the Spectral Theorem120 -- 4.1.5 Spectral Types and the RAGE theorem126 -- 4.1.6 Sectorial forms and form-bounded perturbations128 -- 4.1.7 The min-max principle130 -- 4.1.8 Weyl asymptotics131 -- 4.1.9 Auxiliary results from Sobolev space132 -- 4.1.10 Analytic perturbation theory132 -- 4.1.11 Generalized eigenfunction expansions134 -- 4.2 Some basics from probability theory137 -- 4.2.1 Measurable sets and random variables137 -- 4.2.2 Measure and probability138 -- 4.2.3 Independence 139 -- 4.2.4 Product measures140 -- 4.2.5 Ergodicity 142 -- 4.2.6 Monotone class arguments142 -- 5 Aftermath 145 -- References 147 -- Author Index 161 -- Subject Index 165