Destruction of Anderson localization in nonlinear lattices

我们想研究非线性如何改变无序晶格的局部化性质。这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。两种设置将被深入研究数值：(i)一个初始局部波包在大晶格中的传播和（ii）通过非线性无序层的传输。在后一种情况下，我们将执行一种新的统计分岔分析，以统计方式表征从静态传输到时变传输的预期急剧转变。在这两种情况下，我们都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传输。我们将根据非线性强度、晶格长度和其他参数统计表征这些效应。

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.