ENGLISH

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

By Ivan Veselić (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2008
ISBN
9783540726913, 3540726918, 9783540726890, 3540726896
DOI
10.1007/978-3-540-72691-3
Language
english
Format
PDF
Filesize
784 kB (803045 bytes)
Series
Lecture Notes in Mathematics 1917
Edition
1
Pages
147\154
Library
usenet tech
Time added
2013-03-30 20:00:00
Partial Differential Equations; Dynamical Systems

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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