Random Operators

Michael Aizenman, Simone Warzel

ISBN 10: 1470419130 / ISBN 13: 9781470419134

Published by American Mathematical Society, US, 2015

About this Item

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.

Seller Inventory # LU-9781470419134

Bibliographic Details

• Title: Random Operators
• Publisher: American Mathematical Society, US
• Publication Date: 2015
• Language: English
• ISBN 10: 1470419130
• ISBN 13: 9781470419134
• Binding: Hardback
• Condition: New
• Dimensions: 18.42W x 1.91H x 26.67D centimeters 18.42 centimeters width by 1.91 centimeters height by 26.67 centimeters depth
• Weight: 755 grams

About this title

Synopsis

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.

About the Author

Michael Aizenman, Princeton University, NJ, USA. Simone Warzel, Technische Universitat Munchen, Germany.