Results 11  20
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32
Twoparameter spectral averaging and localization for nonmonotonic random Schrödinger operators
 TRANS. AMER. MATH. SOC
, 2001
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Explicit Finite Volume Criteria For Localization In Continuous Random Media And Applications
 GEOM. FUNCT. ANAL
, 2003
"... We give finite volume criteria for localization of quantum or classical waves in continuous random media. We provide explicit conditions, depending on the parameters of the model, for starting the bootstrap multiscale analysis. A simple application yields localization for Anderson Hamiltonians on th ..."
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Cited by 23 (11 self)
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We give finite volume criteria for localization of quantum or classical waves in continuous random media. We provide explicit conditions, depending on the parameters of the model, for starting the bootstrap multiscale analysis. A simple application yields localization for Anderson Hamiltonians on the continuum at the bottom of the spectrum in an interval of size O() for large , where stands for the disorder parameter. A more sophisticated application proves localization for twodimensional random Schrödinger operators in a constant magnetic field (random Landau Hamiltonians) up to a distance O( B ) from the Landau levels, where B is the strength of the magnetic field.
Wegner estimates and localization for continuum Anderson models with some singular distributions
 Arch. Math. (Basel
, 1998
"... We give a simple geometric proof of Wegner's estimate which leads to a variety of new results on localization for multidimensional random operators. Introduction One of the most important topics in the mathematical theory of disordered solids is localization by which one understands the phenomeno ..."
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Cited by 22 (7 self)
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We give a simple geometric proof of Wegner's estimate which leads to a variety of new results on localization for multidimensional random operators. Introduction One of the most important topics in the mathematical theory of disordered solids is localization by which one understands the phenomenon that states are confined to a finite region in space. This is in sharp contrast to the case of ordered media where states travel to infinity and leave any finite region as time goes to infinity. Mathematically, localization is most commonly described by the occurence of pure point spectrum with exponentially decreasing eigenfunctions for the hamiltonian in question. For Anderson models, i.e. models of the form H(!) = H 0 + X i2\Gamma q i (!)f(\Delta \Gamma i) the general scheme of proof is by now quite well understood. Here e.g. H 0 = \Gamma\Delta +V 0 with \Gammaperiodic V 0 describes a medium with periodicity lattice \Gamma and the sum describes impurities by a random perturbation ...
Operator Kernel Estimates For Functions Of Generalized Schrödinger Operators
 Proc. Amer. Math. Soc
, 2001
"... We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators, a class of semibounded second order partial differential operators of Mathematical Physics, which includes the Schrödinger operator, the magnetic Schrödinger operator, and the classical wave ..."
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Cited by 20 (8 self)
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We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators, a class of semibounded second order partial differential operators of Mathematical Physics, which includes the Schrödinger operator, the magnetic Schrödinger operator, and the classical wave operators (i.e., acoustic operator, Maxwell operator, and other second order partial differential operators associated with classical wave equations). We derive an improved CombesThomas estimate, obtaining an explicit lower bound on the rate of exponential decay of the operator kernel of the resolvent. We prove that for slowly decreasing smooth functions the operator kernels decay faster than any polynomial.
Spectral Localization by Gaussian Random Potentials in MultiDimensional Continuous Space
, 2000
"... this paper is to contribute to the understanding of spectral localization for random Schrdinger operators in multidimensional Euclidean space ..."
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Cited by 19 (4 self)
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this paper is to contribute to the understanding of spectral localization for random Schrdinger operators in multidimensional Euclidean space
Local and Global Continuity of the Integrated Density of States
 COMMUN. PARTIAL DIFFER. EQUATIONS
, 2002
"... The integrated density of states (IDS) N(E) is the distribution function of a nonnegative measure #, the density of states measure (DOS). This measure ..."
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Cited by 13 (3 self)
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The integrated density of states (IDS) N(E) is the distribution function of a nonnegative measure #, the density of states measure (DOS). This measure
Multiscale analysis and localization of random operators
 In Random Schrodinger operators: methods, results, and perspectives. Panorama & Synthèse, Société Mathématique de
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Dynamical delocalization in random Landau Hamiltonians
, 2004
"... We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disorderedbroadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, n ..."
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Cited by 11 (5 self)
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We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disorderedbroadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, namely a boundary point between the localization and delocalization regimes, which we prove to converge to the corresponding Landau level as either the magnetic field or the disorder goes to zero.
Localization In One Dimensional Random Media: A Scattering Theoretic Approach
 COMM. MATH. PHYS
, 2000
"... We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site per ..."
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Cited by 10 (6 self)
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We use scattering theoretic methods to prove exponential localization for random displacement models in one dimension. The operators we consider model both quantum and classical wave propagation. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations. We show that randomly displaced, nonreflectionless single sites lead to localization.