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Random Operators: Disorder Effects on Quantum Spectra and Dynamics
About this Title
Michael Aizenman, Princeton University, Princeton, NJ and Simone Warzel, Technische Universität München, München, Germany
Publication: Graduate Studies in Mathematics
Publication Year:
2015; Volume 168
ISBNs: 978-1-4704-1913-4 (print); 978-1-4704-2783-2 (online)
DOI: https://doi.org/10.1090/gsm/168
MathSciNet review: MR3364516
MSC: Primary 82B44; Secondary 46N50, 47B80, 60H25, 81Q10, 81Q12, 82B10, 82D30
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. Introduction
- Chapter 2. General relations between spectra and dynamics
- Chapter 3. Ergodic operators and their self-averaging properties
- Chapter 4. Density of states bounds: Wegner estimate and Lifshitz tails
- Chapter 5. The relation of Green functions to eigenfunctions
- Chapter 6. Anderson localization through path expansions
- Chapter 7. Dynamical localization and fractional moment criteria
- Chapter 8. Fractional moments from an analytical perspective
- Chapter 9. Strategies for mapping exponential decay
- Chapter 10. Localization at high disorder and at extreme energies
- Chapter 11. Constructive criteria for Anderson localization
- Chapter 12. Complete localization in one dimension
- Chapter 13. Diffusion hypothesis and the Green-Kubo-Streda formula
- Chapter 14. Integer quantum Hall effect
- Chapter 15. Resonant delocalization
- Chapter 16. Phase diagrams for regular tree graphs
- Chapter 17. The eigenvalue point process and a conjectured dichotomy
- Appendix A. Elements of spectral theory
- Appendix B. Herglotz-Pick functions and their spectra