Existence and regularity properties of the integrated density of states of random Schrödinger operators / Ivan Veselić.

By: Veselić, Ivan, 1973-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1917.Publisher: Berlin ; New York : Springer-Verlag, ©2008Description: 1 online resource (x, 142 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540726913; 3540726918; 9783540726890; 3540726896Subject(s): Schrödinger operator | Spectral energy distribution | Quantum theory | Schrödinger, Opérateur de | Distribution spectrale de l'énergie | Théorie quantique | Spectral energy distribution | Quantum theory | Schrödinger, opérateur de | Distribution spectrale de l'énergie | Théorie quantique | Schrödinger operator | Quantum theory | Schrödinger operator | Spectral energy distributionGenre/Form: Electronic books. Additional physical formats: Print version:: Existence and regularity properties of the integrated density of states of random Schrödinger operators.DDC classification: 515/.724 LOC classification: QA3 | .L28 no. 1917ebOther classification: O175. 24 Online resources: Click here to access online
Contents:
Random operators -- Existence of the integrated density of states -- Wegner estimate -- Wegner's original idea. Rigorous implementation -- Lipschitz continuity of the IDS -- A. Properties of the spectral shift function.
Summary: 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 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.
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Includes bibliographical references (pages 113-138) and index.

Random operators -- Existence of the integrated density of states -- Wegner estimate -- Wegner's original idea. Rigorous implementation -- Lipschitz continuity of the IDS -- A. Properties of the spectral shift function.

Print version record.

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 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.

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