On the singular spectrum for adiabatic quasi-periodic Schrodinger operators on the real line

被引：8
作者：
Fedotov, A
Klopp, F
机构：
[1] St Petersburg State Univ, Dept Math Phys, St Petersburg 198904, Russia
[2] Univ Paris 13, Inst Galilee, Dept Math, CNRS,URA 7539, F-93430 Villetaneuse, France
来源：
ANNALES HENRI POINCARE | 2004年 / 5卷 / 05期
关键词：
Mathematical Method; Lyapunov Exponent; Spectral Property; Real Line; Asymptotic Formula;
D O I：
10.1007/s00023-004-0186-4
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we study spectral properties of a family of quasi-periodic Schrodinger operators on the real line in the adiabatic limit. We assume that the adiabatic iso-energetic curves are extended along the momentum direction. In the energy intervals where this happens, we obtain an asymptotic formula for the Lyapunov exponent, and show that the spectrum is purely singular.
引用
收藏
页码：929 / 978
页数：50
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