Ballistic Transport for the Schrodinger Operator with Limit-Periodic or Quasi-Periodic Potential in Dimension Two

被引：9

作者：

Karpeshina, Yulia ^{[1
]}

Lee, Young-Ran ^{[2
]}

Shterenberg, Roman ^{[1
]}

Stolz, Gunter ^{[1
]}

机构：

[1] Univ Alabama Birmingham, Dept Math, Campbell Hall,1300 Univ Blvd, Birmingham, AL 35294 USA

[2] Sogang Univ, Dept Math, 5 Baekbeom Ro, Seoul 121742, South Korea

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2017年 / 354卷 / 01期

基金：

新加坡国家研究基金会; 英国工程与自然科学研究理事会;

关键词：

ABSOLUTELY CONTINUOUS-SPECTRUM; QUANTUM DYNAMICS; ANDERSON LOCALIZATION; TRANSFER-MATRICES; LOWER BOUNDS; EQUATION; DIFFUSION; DOMAINS;

D O I：

10.1007/s00220-017-2911-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove the existence of ballistic transport for the Schrodinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity assumptions on the potential which have been used in prior work to establish the existence of an absolutely continuous component and other spectral properties. The latter include detailed information on the structure of generalized eigenvalues and eigenfunctions. These allow one to establish the crucial ballistic lower bound through integration by parts on an appropriate extension of a Cantor set in momentum space, as well as through stationary phase arguments.

引用

页码：85 / 113

页数：29

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