Results 11  20
of
34
Twoparameter spectral averaging and localization for nonmonotonic random Schrödinger operators
 TRANS. AMER. MATH. SOC
, 2001
"... ..."
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 ..."
Abstract

Cited by 23 (11 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 22 (7 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 20 (8 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
The integrated density of states (IDS) N(E) is the distribution function of a nonnegative measure #, the density of states measure (DOS). This measure
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 ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
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.
Multiscale analysis and localization of random operators
 In Random Schrodinger operators: methods, results, and perspectives. Panorama & Synthèse, Société Mathématique de
"... by ..."
Localization for the Schrödinger operator with a Poisson random potential
, 2006
"... We prove exponential and dynamical localization for the Schrödinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localizat ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
We prove exponential and dynamical localization for the Schrödinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localization results in a prescribed energy interval at the bottom of the spectrum provided the density of the Poisson process is large enough.