03118nam 2200625 450 991048385590332120220514083735.03-540-72691-810.1007/978-3-540-72691-3(CKB)1000000000437255(SSID)ssj0000317595(PQKBManifestationID)11267310(PQKBTitleCode)TC0000317595(PQKBWorkID)10289090(PQKB)10035810(DE-He213)978-3-540-72691-3(MiAaPQ)EBC3062065(MiAaPQ)EBC6711193(Au-PeEL)EBL6711193(OCoLC)1272990285(PPN)123739071(EXLCZ)99100000000043725520220514d2008 uy 0engurnn|008mamaatxtccrExistence and regularity properties of the integrated density of states of random Schrödinger operators /Ivan Veselić1st ed. 2008.Berlin ;Heidelberg :Springer,[2008]©20081 online resource (X, 147 p.) Lecture notes in mathematics ;1917"1617-9692 (electronic ed.)."3-540-72689-6 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.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.Lecture notes in mathematics (Springer-Verlag) ;1917.Schrödinger operatorSpectral energy distributionQuantum theorySchrödinger operator.Spectral energy distribution.Quantum theory.515.724Veselić Ivan1973-312343MiAaPQMiAaPQMiAaPQBOOK9910483855903321Existence and regularity properties of the integrated density of states of random Schrödinger operators230585UNINA