A lower bound for the density of states of the lattice Anderson model

被引：10

作者：

Hislop, Peter D. ^{[1
]}

Mueller, Peter ^{[2
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

[2] Univ Gottingen, Inst Theoret Phys, D-37077 Gottingen, Germany

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 08期

关键词：

random Schrodinger operators; integrated density of states; Wegner estimate; lower bound;

D O I：

10.1090/S0002-9939-08-09361-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Anderson model on the multi-dimensional cubic lattice and prove a positive lower bound on the density of states under certain conditions. For example, if the random variables are independently and identically distributed and the probability measure has a bounded Lebesgue density with compact support, and if this density is essentially bounded away from zero on its support, then we prove that the density of states is strictly positive for Lebesgue-almost every energy in the deterministic spectrum.

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收藏

页码：2887 / 2893

页数：7

相关论文

共 17 条

[1] LOCALIZATION AT LARGE DISORDER AND AT EXTREME ENERGIES - AN ELEMENTARY DERIVATION [J].

AIZENMAN, M ;

MOLCHANOV, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 157 (02) :245-278

[2]

Carmona R., 1990, SPECTRAL THEORY RAND, DOI 10.1007/978-1-4939-0512-6_4

[3] An optimal wegner estimate and its application to the global continuity of the integrated density of states for random Schrodinger operators [J].

Combes, Jean-Michel ;

Hislop, Peter D. ;

Klopp, Frederic .

DUKE MATHEMATICAL JOURNAL, 2007, 140 (03) :469-498

[4] LOCALIZATION FOR SOME CONTINUOUS, RANDOM HAMILTONIANS IN D-DIMENSIONS [J].

COMBES, JM ;

HISLOP, PD .

JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 124 (01) :149-180

[5] Existence of the density of states for multi-dimensional continuum Schrodinger operators with Gaussian random potentials [J].

Fischer, W ;

Hupfer, T ;

Leschke, H ;

Muller, P .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 190 (01) :133-141

[6] The absolute continuity of the integrated density of states for magnetic Schrodinger operators with certain unbounded random potentials [J].

Hupfer, T ;

Leschke, H ;

Müller, P ;

Warzel, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 221 (02) :229-254

[7]

JESKE F, 1992, THESIS RUHR U BOCHUM

[8] Spectral properties of the Laplacian on bond-percolation graphs [J].

Kirsch, W ;

Müller, P .

MATHEMATISCHE ZEITSCHRIFT, 2006, 252 (04) :899-916

[9] SMALL PERTURBATIONS AND THE EIGENVALUES OF THE LAPLACIAN ON LARGE BOUNDED DOMAINS [J].

KIRSCH, W .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 101 (03) :509-512

[10] THE STABILITY OF THE DENSITY OF STATES OF SCHRODINGER OPERATOR UNDER VERY SMALL PERTURBATIONS [J].

KIRSCH, W .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 1989, 12 (03) :383-391