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Mathematics Existence and Regularity Properties of the Integrated Density of States of Random Schr?dinger Operators
Posted on 2010-04-12
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More Ivan Veselic "Existence and Regularity Properties of the Integrated Density of States of Random Schr?dinger Operators" The theory of random Schr?dinger 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 left, 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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