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Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators

  • Ivan Veselić

Part of the Lecture Notes in Mathematics book series (LNM, volume 1917)

Table of contents

  1. Front Matter
    Pages I-X
  2. Pages 1-11
  3. Pages 45-56
  4. Back Matter
    Pages 99-146

About this book

Introduction

The theory of random Schrödinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids. Apart from its importance in physics, it is a multifaceted subject in its own right, drawing on ideas and methods from various mathematical disciplines like functional analysis, selfadjoint operators, PDE, stochastic processes and multiscale methods.
The present text describes in detail a quantity encoding spectral features of random operators: the integrated density of states or spectral distribution function. Various approaches to the construction of the integrated density of states and the proof of its regularity properties are presented.

The setting is general enough to apply to random operators on Riemannian manifolds with a discrete group action. References to and a discussion of other properties of the IDS are included, as are a variety of models beyond those treated in detail here.

Keywords

PDE Random operators Stochastic processes coding quantum theory of solids spectral density function statistical mechanics stochastic process

Authors and affiliations

  • Ivan Veselić
    • 1
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-72691-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-72689-0
  • Online ISBN 978-3-540-72691-3
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site