9781470419134-1470419130-Random Operators: Disorder Effects on Quantum Spectra and Dynamics (Graduate Studies in Mathematics)

Random Operators: Disorder Effects on Quantum Spectra and Dynamics (Graduate Studies in Mathematics)

ISBN-13: 9781470419134
ISBN-10: 1470419130
Author: Michael Aizenman, Simone Warzel
Publication date: 2015
Publisher: American Mathematical Society
Format: Hardcover 326 pages
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Book details

ISBN-13: 9781470419134
ISBN-10: 1470419130
Author: Michael Aizenman, Simone Warzel
Publication date: 2015
Publisher: American Mathematical Society
Format: Hardcover 326 pages

Summary

Acknowledged authors Michael Aizenman, Simone Warzel wrote Random Operators: Disorder Effects on Quantum Spectra and Dynamics (Graduate Studies in Mathematics) comprising 326 pages back in 2015. Textbook and eTextbook are published under ISBN 1470419130 and 9781470419134. Since then Random Operators: Disorder Effects on Quantum Spectra and Dynamics (Graduate Studies in Mathematics) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

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.

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