Non Hermitian dynamics of disordered media and interacting atomic Bose-Einstein Condensates

波在复杂介质中的传播是一个跨学科的问题，涉及到电子和原子物质波，以及用于传输能量和信息的光传播等不同领域。尽管存在这种多样性，这些系统的波特征提供了一个共同的框架来理解它们的传输特性，并经常导致新的应用。在这个项目中，我们的研究重点是理解无序介质中的波传播，同时我们研究由于克尔效应或原子-原子相互作用引起的非线性如何影响输运。具体而言，我们解决了以下问题：（a）由于光滑关联无序散射导致的半导体纳米结构中电子流的分支;（B）光子在具有反线性对称性的耦合波导中的传播;（c）具有增益/损耗的光晶格中原子BEC的非厄米动力学;（d）小光学晶格中BEC的混沌散射和（e）无序非线性环形几何中的Aharonov-Bohm振荡。

The propagation of waves through complex media is an interdisciplinary problem that addresses areas as diverse as electronic and atomic-matter waves, to light propagation used to transmit energy and information. Despite this diversity, the wave character of these systems provides a common framework for understanding their transport properties and often leads to new applications. In this project, we focus our research efforts in understanding wave propagation in disordered media while at the same time we investigate how non-linearities due to Kerr effect or due to atom-atom interactions affect the transport. Specifically, we address the following questions : (a) branching of electron flow in semiconductor nanostructures due to scattering from smoothly correlated disorder; (b) propagation of photons in coupled waveguides with anti-linear symmetries; (c) non-hermitian dynamics of atomic BECs in optical lattices with gain/loss; (d) chaotic scattering from a BEC loaded in small optical lattices and (e) Aharonov-Bohm oscillations in disordered non-linear ring geometries.