一维非均匀非线性系统的波包扩散性质的研究

项目名称： 一维非均匀非线性系统的波包扩散性质的研究

项目编号： No.11305045

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 张振俊

作者单位： 河海大学

项目金额： 22万元

中文摘要： 随着冷原子技术的发展，玻色-爱因斯坦凝聚体（BECs）在各种光学势场中膨胀的实验成为当今的一个研究热点。在理论上，BECs的膨胀过程可以用Gross-Pitaevskii(GP)方程描述，这个方程中出现了由平均场近似而产生的非线性作用项。因此，对这类非线性系统的理论研究正受到极大的关注。其中一个重要的领域是对波包扩散性质的研究。目前，对该领域的研究主要集中于空间均匀的非线性作用的情况。而在实验上，已经可以调制出其它分布类型的非线性作用。为此，本项目将采用数值模拟的方法研究：无序链、准周期链、以及具有超级扩散(Hyperdiffusion)行为的非均匀链在各种分布类型的非线性作用下的波包扩散性质。通过这些研究，不仅可以掌握这类复杂系统所具有的输运行为，而且可以为BECs等实验的开展提供指导，在理论上和实验上都具有重要的学术价值。

中文关键词： 一维；非线性；扩散；标度律；热化

英文摘要： Recently, owe to the impressive technological progress in experiments with cold atoms, the experimental studies on Bose-Einstein condensates(BECs) expansions in the optical lattices have been one of the most active fields. The evolution of BECs can be described by the Gross-Pitaevskii(GP) equation, which includes a cubic nonlinear term that represents the mean-field interaction. Therefore, the theoretical work on the complex nonlinear systems has drawn a great deal of attention. One of the important topic of this field is to study the diffusion properties of wave packet. Recent research in this field primary focuses on the spatial uniform distribution of nonlinearity. On the experimental side, other spatial distributions of nonlinearity have been modulated in BECs by dint of the Feshbach resonances through nonuniform magnetic fields. Thus, in this project, we will study the propagation properities of wave packet in disordered chain, in quasiperiodic chain, and in nonuniform chain that has hyperdiffusive behavior with various spatial distributions of nonlinearity, respectively. The results not only can provide common ground for understanding transport properties but also can be useful in motivating and guiding experiments on the expansion of BECs in optical lattices and hence has great academic value both on the

英文关键词： One-dimension；Nonlinearity；Duffusion；Scaling law；Thermalization