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Pure point spectrum of the floquet Hamiltonian for the quantum harmonic oscillator under time quasi-periodic perturbations

被引：48
|
作者：
Wang, W. -M. [1 ,2 ]
机构：
[1] Univ Paris 11, Dept Math, F-91405 Orsay, France
[2] Univ Massachusetts, Dept Math, Amherst, MA 01003 USA
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2008年 / 277卷 / 02期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/s00220-007-0379-z
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We prove that the 1-d quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their 1983 paper [EV] in the general quasi-periodic setting. The motivation of the present paper also comes from construction of quasi-periodic solutions for the corresponding nonlinear equation.
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页码：459 / 496
页数：38
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