Analytical Localization Lengths in an One-Dimensional Disordered Electron System

被引：0

作者：

Rauh, Alexander ^{[1
]}

机构：

[1] Carl von Ossietzky Univ Oldenburg, Inst Phys, D-26111 Oldenburg, Germany

来源：

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 2009年 / 64卷 / 3-4期

关键词：

Anderson Localization; Lyapunov Exponent; Transfer Matrix; Functional Equation; WAVE-FUNCTIONS; DIFFUSION; ABSENCE;

D O I：

10.1515/zna-2009-3-407

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

Analytical approximations of the Lyapunov exponent are derived for a random displacement model with equal potential barriers and random positions of the scatterers. Two asymptotic regions are considered corresponding to high and low reflectivity of the single scattering potential. The analytical results are in terms of a distribution function W for certain phases of the transfer matrices. A functional equation for W is derived and numerically solved. This serves to validate the analytical asymptotic formulas which turn out to be accurate in the high and low reflectivity regions with dimensionless wave number K < 2 and K > 6, respectively. The high wave number asymptotics allows for an analytical examination of the sufficient conditions for Anderson localization.

引用

页码：205 / 221

页数：17

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