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.
| ISBN: | 9781470419134 |
| Publication date: | 30th December 2015 |
| Author: | Michael Aizenman, Simone Warzel |
| Publisher: | American Mathematical Society |
| Format: | Hardback |
| Pagination: | 320 pages |
| Series: | Graduate Studies in Mathematics |
| Genres: |
Mathematical physics Calculus and mathematical analysis Probability and statistics Applied mathematics |
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.
Random Operators features in the following genres: Mathematical physics, Calculus and mathematical analysis, Probability and statistics, Applied mathematics
Random Operators is available in Hardback
Random Operators was written by Michael Aizenman, Simone Warzel and published by American Mathematical Society
Random Operators has 320 pages
Yes it is part of Graduate Studies in Mathematics series