Eigenfunction statistics in the localized Anderson model

被引：30
作者：
Killip, Rowan
Nakano, Fumihiko
机构：
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
[2] Kochi Univ, Fac Sci, Dept Math & Informat Sci, Kochi 7808520, Japan
来源：
ANNALES HENRI POINCARE | 2007年 / 8卷 / 01期
基金：
日本学术振兴会; 美国国家科学基金会;
关键词：
D O I：
10.1007/s00023-006-0298-0
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider the localized region of the Anderson model and study the distribution of eigenfunctions simultaneously in space and energy. In a natural scaling limit, we prove convergence to a Poisson process. This provides a counterpoint to recent work, [9], which proves repulsion of the localization centres in a subtly different regime.
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收藏
页码：27 / 36
页数：10
相关论文
共 11 条
[1]   Finite-volume fractional-moment criteria for Anderson localization [J].
Aizenman, M ;
Schenker, JH ;
Friedrich, RM ;
Hundertmark, D .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 224 (01) :219-253
[2]   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
[3]   ABSENCE OF DIFFUSION IN THE ANDERSON TIGHT-BINDING MODEL FOR LARGE DISORDER OR LOW-ENERGY [J].
FROHLICH, J ;
SPENCER, T .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 88 (02) :151-184
[4]  
KALLENBERG O, 1986, RANDOM MEASURES
[5]  
Klein A, 2006, J STAT PHYS, V122, P95, DOI 10.1007/s10955-005-8009-7
[6]   Local fluctuation of the spectrum of a multidimensional Anderson tight binding model [J].
Minami, N .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1996, 177 (03) :709-725
[7]  
MOLCANOV SA, 1981, COMMUN MATH PHYS, V78, P429, DOI 10.1007/BF01942333
[8]  
NAKANO F, IN PRESS J STAT PHYS
[9]   CYCLIC VECTORS IN THE ANDERSON MODEL [J].
SIMON, B .
REVIEWS IN MATHEMATICAL PHYSICS, 1994, 6 (5A) :1183-1185
[10]   A NEW PROOF OF LOCALIZATION IN THE ANDERSON TIGHT-BINDING MODEL [J].
VONDREIFUS, H ;
KLEIN, A .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1989, 124 (02) :285-299
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