Growth of Sobolev Norms and Controllability of the Schrodinger Equation

被引：46
作者：
Nersesyan, Vahagn [1 ]
机构：
[1] Univ Paris 11, Math Lab, F-91405 Orsay, France
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2009年 / 290卷 / 01期
关键词：
SYSTEMS; TIME; EIGENVALUES;
D O I：
10.1007/s00220-009-0842-0
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper we obtain a stabilization result for both linear and nonlinear Schrodinger equations under generic assumptions on the potential. Then we consider the Schrodinger equations with a potential which has a random time-dependent amplitude. We show that if the distribution of the amplitude is sufficiently non-degenerate, then any trajectory of the system is almost surely non-bounded in Sobolev spaces.
引用
收藏
页码：371 / 387
页数：17
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