Long Time Anderson Localization for the Nonlinear Random Schrödinger Equation

被引：0

作者：

W.-M. Wang

Zhifei Zhang

机构：

[1] Universite Paris Sud,Departement de Mathematique

[2] Peking University,School of Mathematical Sciences

来源：

Journal of Statistical Physics | 2009年 / 134卷

关键词：

Anderson localization; Birkhoff normal form;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove long time Anderson localization for the nonlinear random Schrödinger equation for arbitrary ℓ2 initial data, hence giving an answer to a widely debated question in the physics community. The proof uses a Birkhoff normal form type transform to create a barrier where there is essentially no propagation. One of the new features is that this transform is in a small neighborhood enabling us to treat “rough” data, where there are no moment conditions. The formulation of the present result is inspired by the RAGE theorem.

引用

页码：953 / 968

页数：15

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