Destruction of Anderson localization in nonlinear lattices

我们想研究无序晶格的局域化性质是如何被非线性所改变的。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。我们将对两种情况进行深入的数值研究：(I)初始局域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叉分析，以统计地描述预期的从静态到依赖于时间的传输的急剧转变。在这两种情况下，我们都希望观察到非线性对局域化的破坏，这应该分别导致无限扩散和增强的传输。我们将根据非线性强度、晶格长度和其他参数对这些效应进行统计表征。

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.