PRIMALIGHT, Faculty of Electrical Engineering, Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia.
Sci Rep. 2013;3:2359. doi: 10.1038/srep02359.
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter.
我们采用非线性量子受迫转子模型研究多维量子混沌中的能量输运。这个问题在从安德森局域化到经典和量子波的时间反演等多个科学领域都有深远的意义。我们从一系列平行的数值模拟开始分析，结果显示出出乎意料和反常的行为。我们通过具有李群和孤子理论特征的完全解析方法来解决这个问题，证明了系统中存在一种普遍的、非线性增强的能量扩散，这种扩散完全由孤子波维持。用不同模型进行的数值模拟与普遍预测完全一致。我们还在二维偶极玻色-爱因斯坦凝聚体（BEC）中讨论了一个实际实验。除了在基本层面上的明显意义外，我们的结果还表明，孤子可以成为实现物质增强输运的新系统的构建块。
