The Integrated Density of States for Some Random Operators with Nonsign Definite Potentials
Peter D. Hislop,Frédéric Klopp +1 more
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In this paper, the integrated density of states of random Anderson-type additive and multiplicative perturbations of deterministic background operators for which the single-site potential does not have a fixed sign was studied.About:
This article is published in Journal of Functional Analysis.The article was published on 2002-10-20 and is currently open access. It has received 115 citations till now. The article focuses on the topics: Operator theory & Randomness.read more
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A characterization of the Anderson metal-insulator transport transition
François Germinet,Abel Klein +1 more
TL;DR: In this article, the Anderson metal-insulator transition for random Schrodinger operators is investigated and the strong insulator region is defined as the part of the spectrum where the random operator exhibits strong dynamical localization in the Hilbert-Schmidt norm.
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A comprehensive proof of localization for continuous Anderson models with singular random potentials
François Germinet,Abel Klein +1 more
TL;DR: In this article, the authors studied continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support and proved the existence of a strong form of Anderson localization at the bottom of the spectrum, which includes Anderson localization with exponentially decaying eigenfunctions with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution), decay of eigfunctions correlations, and decay of the Fermi projections.
The Integrated Density of States for Random Schrödinger Operators
Werner Kirsch,Bernd Metzger +1 more
TL;DR: A survey of the theory of the integrated density of states (IDS) of random Schrodinger operators can be found in this paper, where the authors focus on the asymptotic behavior of the IDS at the boundary of the spectrum.
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Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators
TL;DR: The theory of random Schrodinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids as mentioned in this paper, and 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.
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Explicit finite volume criteria for localization in continuous random media and applications
François Germinet,Abel Klein +1 more
TL;DR: In this article, finite volume criteria for quantum or classical wave localization in continuous random media were given for the case of Anderson Hamiltonians on the continuum and random Schrodinger operators in a constant magnetic field.
References
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Trace ideals and their applications
TL;DR: In this paper, Calkin's theory of operator ideals and symmetrically normed ideals convergence theorems for trace, determinant, and Lidskii's theorem are discussed.
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Spectral Theory of Self-Adjoint Operators in Hilbert Space
M. S. Birman,M. Z. Solomjak +1 more
TL;DR: In this article, the authors present an algebra of continuous linear operators on Hilbert spaces, which is a generalization of the notion of a continuous linear operator on the space L 2 (Rm, Cm).
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Brownian motion and harnack inequality for Schrödinger operators
Michael Aizenman,Barry Simon +1 more
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Mathematical Scattering Theory: General Theory
TL;DR: In this article, the spectral shift function (SSF) and the trace formula were used for WO scattering for relatively smooth perturbations, and the general setup in stationary scattering theory for perturbation of trace class type.
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Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators
J. M. Combes,Lawrence E Thomas +1 more
TL;DR: In this article, O'Connor's approach to spatial exponential decay of eigenfunctions for multiparticle Schrodinger Hamiltonians is developed from the point of view of analytic perturbations with respect to transformation groups.