Coherent transport of waves in disordered systems with nonlinearity and interactions

我们想研究波在随机介质中传播时无序和非线性或相互作用之间的相互作用。我们特别感兴趣的相干效应，由于波的干扰，这是众所周知的情况下，线性或非相互作用的系统，可以修改，甚至完全改变的字符相比，不相干的政权波输运，例如把扩散到本地化。通过非线性图解散射理论结合数值模拟，我们将分析非线性和相互作用对这些相干效应的影响，包括经典非线性介质中的波传播和相互作用的多粒子量子系统。特别是，我们要检查是否-与通常的看法相反-波本地化可以有利，而不是阻碍适当选择的非线性，如我们以前的工作所建议的非线性相干后向散射。

We want to investigate the interplay between disorder and nonlinearity or interactions in the propagation of waves through random media. We are especially interested in coherent effects due to wave interference, which, as well known from the case of linear or non-interacting systems, may modify or even completely change the character of wave transport as compared to the incoherent regime, for example turn diffusion into localization. By means of nonlinear diagrammatic scattering theory in connection with numerical simulations, we will analyze the impact of nonlinearities and interactions on those coherent effects, both for propagation of waves in classical nonlinear media and for interacting many-particle quantum systems. In particular, we want to examine whether - contrary to common belief - wave localization can be favored rather than hindered by properly chosen nonlinearities, as suggested by our previous work on nonlinear coherent backscattering.