Copy of Generation of spatial dispersive shocks in the supersonic flow of Bose-Einstein condensate past an obstacle

玻色-爱因斯坦凝聚体超音速流过障碍物时产生空间色散激波的副本

• 批准号: EP/D077559/1
• 负责人: Gennady El
• 金额: $ 1.44万
• 依托单位: Loughborough University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD077559%2F1
• 关键词: Copy; Generation; spatial; dispersive; shocks

Bose-Einstein condensate (BEC) represents a unique state of matter demonstrating quantum properties on macroscopic spatial scales. After the first experimental realisation of the BEC of dilute alkali gases in 1995 (followed by the Nobel Prize for Physics in 2001) this new physical object has attracted a great deal of attention of specialists in nonlinear wave dynamics. The reason of this interest is, in particular, connected with a possibility to conduct very subtle experiments where so-called matter waves are realised. These waves represent a manifestation of quantum behavior at macroscopic scales and, unlike most quantum mechanics effects, are essentially nonlinear. Indeed, in the experiments, a number of effects have been observed which cannot be explained using conventional linear wave theory. One of the series of recent experiments of JILA Cornell group (Boulder, Colorado) on BEC flow past macroscopic obstacles revealed tthe existence of specific shock waves in the BEC similar to the so-called collisionless shocks in rarefied plasmas and undular bores on shallow water. Such dispersive shock waves consist of a large number of interacting solitons (nonlinear solitary waves with the unique particle-like behaviour). The aim of the present project is, using the Gross-Pitaevskii equation, which is a general mathematical model describing BEC dynamics, to construct an analytical theory of the dispersive shock waves in BEC. This theory will enable one to understand and quantitatively explain results of the mentioned recent experiments on the BEC flows past obstacles and, possibly, to predict new nonlinear dispersive wave effects in BEC. The project will require a substantial development of the mathematical theory of the Gross-Pitaevskii equation, which could be used by applied mathematicians and physicists in other physical contexts.

玻色-爱因斯坦凝聚体（BEC）是一种在宏观空间尺度上表现出量子特性的独特物质状态。在1995年第一次实验实现稀碱气体的BEC（随后在2001年获得诺贝尔物理学奖）之后，这个新的物理对象吸引了非线性波动力学专家的大量关注。这种兴趣的原因特别是与进行非常微妙的实验的可能性有关，在这种实验中实现了所谓的物质波。这些波代表了宏观尺度下量子行为的表现，与大多数量子力学效应不同，它们本质上是非线性的。事实上，在实验中，已经观察到了许多无法用传统的线性波理论解释的效应。JILA Cornell小组（科罗拉多博尔德）最近对BEC流通过宏观障碍物的一系列实验之一揭示了BEC中存在类似于稀薄等离子体中所谓的无碰撞激波和浅水中的波状孔的特殊激波。这种色散激波由大量相互作用的孤立子（具有独特的粒子行为的非线性孤立波）组成。本项目的目的是，使用Gross-Pitaevskii方程，这是一个通用的数学模型描述BEC动力学，建立一个分析理论的色散冲击波在BEC。这一理论将使人们能够理解和定量地解释上述最近的实验结果的BEC流过去的障碍物，并可能预测新的非线性色散波效应BEC。该项目将需要大幅度发展Gross-Pitaevskii方程的数学理论，应用数学家和物理学家可以在其他物理环境中使用。