Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators
Publication year: 2008
: 978-3-540-72691-3
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.
: Mathematics and Statistics, PDE, Random operators, Stochastic processes, coding, quantum theory of solids, spectral density function, statistical mechanics, stochastic process, partial differential equations
