PURE POINT SPECTRUM UNDER 1-PARAMETER PERTURBATIONS AND INSTABILITY OF ANDERSON LOCALIZATION

被引：39

作者：

GORDON, AY

机构：

[1] Warshavskoye shosse, MITPAN, Moscow, 113556, 79

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1994年 / 164卷 / 03期

关键词：

D O I：

10.1007/BF02101488

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider a selfadjoint operator, A, and a selfadjoint rank-one projection, P, onto a vector, psi, which is cyclic for A. We study the set of all eigenvalues of the operator A(t) = A + tP (t is-an-element-of R) that belong to its essential spectrum (which does not depend on the parameter t). We prove that this set is empty for a dense set of values of t. Then we apply this result or its idea to questions of Anderson localization for 1-dimensional Schrodinger operators (discrete and continuous).

引用

页码：489 / 505

页数：17

共 14 条

[1]

Akhiezer N.I., 1963, THEORY LINEAR OPERAT, VII

[2] ANDERSON LOCALIZATION FOR THE 1-D DISCRETE SCHRODINGER OPERATOR WITH 2-FREQUENCY POTENTIAL [J].