Quantum vortex reconnections in trapped Bose-Einstein condensates

长，几乎一维的结构（细丝）在宇宙中无处不在，由原子链（大分子）或集中的场线区域（流体中的涡旋线，导电等离子体中的磁通管）组成。细丝出现在蛋白质和DNA的微观尺度上，通过龙卷风、尘暴和飞机和船只后面的轨迹的中等尺度，直到外层空间中形成恒星的云的巨大尺度。当两根细丝彼此靠近时，它们可以分裂并重新组合，形成交换的丝。这样的重连接事件不仅改变了细丝本身的几何形状，而且还改变了底层的拓扑结构（两个相互连接的环与两个分离的环不同的性质）。因此，更好地理解重连对于自然科学和工程中的许多问题（例如，流体的能量如何通过重连传播）都是至关重要的。由于在许多不同的物理环境和许多尺度上产生了重新连接，人们很自然地会问，是否有任何行为是普遍的，这样就可以寻求一个共同的理解框架。例如，流体重联过程中的能量损失与等离子体重联过程中的能量损失直接类似，尽管能量损失的物理来源不同（流体中的粘度和等离子体中的电阻率）。科学界争论的另一个例子是，在重连过程中，被称为螺旋度的细丝的盘绕、扭曲和连接的测量是否守恒，以及细丝的复杂纠缠结是否会以依赖于拓扑而不是系统的物理性质的方式衰减或解开。我们对重连的理解仍处于起步阶段，将受益于对重连的详细定量测量，以及对不同科学学科间重连的比较。在这种情况下，捕获原子玻色-爱因斯坦凝聚体（BECs）为研究重连提供了理想的试验场。BECs是原子气体，冷却到绝对零度以上几亿分之一度。在这里，模糊的量子力学定律支配并将气体转化为量子流体。这种流体非常简单：日常流体具有粘度，可以形成任何大小和形状的龙卷风，而量子流体没有粘度，它们的龙卷风具有固定的大小和形状。这使得它们更容易概念化、建模和理解。更重要的是，实验人员能够控制和操纵流体及其漩涡，达到很高的精度。我们最近与意大利Trento的一个实验小组合作开展了初步工作，不仅首次展示了BECs中的重新连接，而且揭示了新的和意想不到的重新连接形式。受此启发，我们将在bec提供的理想环境下对涡旋重连进行详细的计算机模拟，准确确定重连是如何发生的，以及它们的后果是什么。然后，通过比较不同环境下（普通流体、等离子体和大分子）的行为，我们将探索是否存在普遍的行为（例如，如果重新连接的链之间的距离与时间的普遍幂律有关，或者如果能量损失与打结的数量有关），探测不同系统中能量和拓扑之间的关系。为了在科学界传播我们的研究成果，我们将组织一个跨学科的研讨会，与来自原子物理学、天体物理学、流体动力学、结理论的顶级专家进行重新连接，以期建立一个共同的图景。与特伦托正在进行的实验密切合作将指导我们的理论研究，并为我们的发现提供即时的实验测试。

Long, almost one dimensional structures (filaments) are ubiquitous in the universe, consisting of chains of atoms (macromolecules) or regions of concentrated field lines (vortex lines in fluids, magnetic flux tubes in electrically conducting plasmas). Filaments occur at the microscopic scale of proteins and DNA, through the intermediate scales of tornadoes, dust devils and the trails behind planes and boats, up to the huge scales of the star-forming clouds in outer space. When two filaments come close to each other, they can split and recombine, having exchanged strands. Such reconnection events not only change the geometry of the filaments themselves but they also change the underlying topology (the property for which two rings which are linked to each other are different from two rings which are separated). A better understanding of reconnections is therefore crucial to many problems in the natural sciences and in engineering (for example, how the energy of a fluid is spread by reconnections). With reconnections arising across many distinct physical contexts and over many scales, it is natural to ask whether any behaviours are universal, such that a shared framework of understanding can be sought. For example, the loss of energy during a reconnection in a fluid is directly analogous to that which occurs during a reconnection in a plasma despite different physical origins of the loss of energy (viscosity in the fluid and electrical resistivity in the plasma). Other examples debated in the scientific community are whether a measure of the coiling, twisting and linking of the filaments, termed the helicity, is conserved during reconnections, and whether complicated tangled knots of filaments may decay or disentangle in ways which depend on the topology rather than the physical nature of the system. Our understanding of reconnections is still in its infancy and would benefit from detailed quantitative measurements of reconnections, and from comparison of reconnections across different scientific disciplines.In this context, trapped atomic Bose-Einstein condensates (BECs) provide an ideal testing ground to study reconnections. BECs are gases of atoms, cooled to within a few billionths of a degree above absolute zero. Here the blurry laws of quantum mechanics rule and transform the gas into a quantum fluid. This type of fluid is remarkable in its simplicity: while everyday fluids possess viscosity and can form tornadoes of any size or shape, quantum fluids have no viscosity and their tornadoes have a fixed size and shape. This makes them easier to conceptualise, model and understand. What is more, experimentalists are able to control and manipulate the fluid, and its vortices, to a high level of precision. Our recent preliminary work in collaboration with an experimental group in Trento, Italy, not only demonstrated reconnections in BECs for the first time, but also revealed new and unexpected forms of reconnections. Motivated by this, we will perform detailed computer simulations of vortex reconnections in the ideal context provided by BECs, determining exactly how reconnections occur and what their consequences are. Then, by comparing to the behaviour in different settings (ordinary fluids, plasmas and macromolecules) we will probe whether universal behaviours do exist (for example, if the distance between reconnecting strands scales with time with a universal power law, or if energy losses relate to the amount of knottedness), probing the relation between energy and topology in different systems. To disseminate our results across scientific communities, we will organise an interdisciplinary workshop on reconnections with the top experts from atomic physics, astrophysics, fluid dynamics, knot theory, with a view to building a common picture. Close collaboration with the ongoing experiment at Trento will guide our theoretical studies and provide immediate experimental tests of our findings.