Destruction of Anderson localization in nonlinear lattices

非线性晶格中安德森局域化的破坏

• 批准号: 93017253
• 负责人: Professor Dr. Arkady Pikovsky
• 金额: --
• 依托单位: Institut für Physik und Astronomie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2008
• 资助国家: 德国
• 起止时间: 2007-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/93017253?language=en
• 关键词: Destruction; Anderson; localization; nonlinear; lattices

We want to study how the localization properties of disordered lattices are modified by nonlinearity. Relevant experimental realizations of such systems include photonic lattices, Bose-Einstein condensate, and mechanical disordered systems. Two setups will be intensively studied numerically: (i) a spreading of an initially localized wave packet in a large lattice and (ii) a transmission through a nonlinear disordered layer. In the latter case we will perform a novel statistical bifurcation analysis to characterize statistically an expected sharp transition from static to time-dependent transmission. In both cases we expect to observe destruction of the localization by the nonlinearity, what should lead to an unbounded diffusion and to an enhanced transmission, respectively. We will statistically characterize these effects in dependence on the nonlinearity strength, length of the lattice, and other parameters.

我们想研究无序晶格的局域化性质如何被非线性所改变。此类系统的相关实验实现包括光子晶格、玻色-爱因斯坦凝聚和机械无序系统。两个设置将深入研究数值：（i）一个最初本地化的波包在一个大的晶格和（ii）通过一个非线性无序层的传输的传播。在后一种情况下，我们将执行一个新的统计分岔分析，统计特征的预期急剧转变，从静态到时间依赖性传输。在这两种情况下，我们期望观察到非线性对局域化的破坏，这将分别导致无界扩散和增强的传输。我们将根据非线性强度、晶格长度和其他参数来统计表征这些效应。