Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators (Lecture Notes in Mathematics)

Description

Publisher: Springer; 1 edition
Language: English
ISBN: 3540726896
Paperback: 146 pages
Data: January 2008
Format: PDF
Description: 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.

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