Vortices and solitons in finite-temperature Bose-Einstein condensates

近年来，超冷气体的性质引起了人们的极大关注。这种兴趣是由实验引起的，这些实验通过使用磁场和激光的组合，能够将稀释气体的温度限制在绝对零度以上十亿分之一度以下。在这样的温度下，可能会出现我们日常生活中不熟悉的奇怪情况。例如，如果温度足够低，原子可能会经历一种叫做玻色-爱因斯坦凝聚的现象，在这种现象下，所有的原子往往会一起运动。这导致了一些相当惊人和令人着迷的行为，例如气体在没有阻力的情况下流动的能力。这种类似于电流流过超导体的性质被称为超流性。超冷原子的一个很好的特点是它们可以很容易地控制和直接成像，并且在理论上相对容易处理，所以是非常好的研究超流体行为的系统。尤其令人感兴趣的是漩涡，这是流体中常见的特征，有时会以漩涡或龙卷风的形式出现。当它们被旋转或被迫太快地流过障碍物时，它们就会出现在超流体中。然后，漩涡可以与不属于超流体一部分的原子相互作用，产生摩擦力，从而对流动产生阻力。因此，涡旋是超流破裂的重要组成部分，我们的研究将主要集中在研究这些相互作用上。研究这个问题的一个强烈动机是，在其他系统中也发现了类似的行为，比如液氦或中子星内部，但在理论上还没有完全理解。因此，通过研究这个系统并与实验进行比较，我们期待这将为这些其他系统提供有价值的见解。

In recent years there has been a great deal of attention paid to the properties of ultracold gases. This interest has been prompted by experiments that, by using a combination of magnetic fields and lasers, have been able to confine and cool dilute gases down to temperatures billionths of a degree above absolute zero. At these temperatures strange situations can arise that are unfamilar to us in our everyday lives. For example, if the temperature is low enough the atoms can undergo a phenomenon called Bose-Einstein condensation, where all of the atoms tend to move together. This leads to some rather startling and fascinating behaviour, such as the ability of the gas to flow without resistance. This property, which is similar to the flow of an electric current through a superconductor, is known as superfluidity. A nice feature of ultracold atoms is that they can be easily controlled and imaged directly, and are relatively simple to treat theoretically, so are very good systems in which to study superfluid behaviour.The proposed research will theoretically study the properties of these superfluid ultracold gases. Of particular interest are vortices, which are a familiar feature in fluids where they sometimes appear as whirlpools or tornados. They appear in superfluids when they are rotated or forced to flow past an obstacle too quickly. The vortices can then interact with atoms that are not part of the superfluid, creating a frictional force and therefore a resistance to the flow. So, the vortices are an important component in the breakdown of superfluidity, and our research will be mainly concerned with studying these interactions. A strong motivation for research into this problem is that similar behaviour is found in other systems, such as liquid helium or inside neutron stars, but isn't fully understood theoretically. So by studying this system and comparing to experiments we expect that this will provide valuable insights into these other systems.