Description
Book 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.
Trade ReviewIt 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
Table of Contents
- Introduction
- 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
