Knot solitons in superconductors? A definitive test of the Babaev-Faddeev-Niemi hypothesis

当导电的带电粒子（通常是电子）相互配对并开始表现得更像流体时，超导现象就发生了。在一些超导体中，这种配对可以以不止一种方式发生，并且在材料中有不止一种这样的流体共存。这种情况用多分量金兹堡-朗道理论进行了数学描述。近年来，人们已经认识到，额外流体的存在可能导致惊人的和完全意想不到的新效应。理论物理学家Babaev、Faddeev和Niemi通过一种巧妙但颇具争议的数学论证认为，双组分金兹堡-朗道理论可以简化为一个表面上完全无关的数学模型，称为Faddeev- skyrme模型。这将是非常令人兴奋的，因为faddev - skyrme模型已知拥有所谓的“结孤子”：稳定的、局部的能量块，由于它们所在的场变量在空间中是打结的，它们不会消散。撇开它们内在的数学兴趣不谈，这种结孤子的出现在凝聚态物理中是前所未有的。所提出的研究的主要目的是明确回答Babaev-Faddeev-Niemi假设是否正确。他们争论的关键是观察到，当双分量金兹堡-朗道模型中某些场之间的直接耦合被忽略（或关闭）时，模型就会简化为faddev - skyrme模型。我们将通过模拟金兹堡-朗道模型的行为来直接验证这一说法，因为耦合慢慢地重新打开。这将需要在白玫瑰并行计算网格上进行大规模计算机模拟。

Superconductivity occurs when the charged particles which conduct electricity (usually electrons) pair off with one another and start to behave rather like a fluid. In some superconductors, this pairing can occur in more than one way, and one has more than one such fluid coexisting in the material. This situation is described mathematically by multicomponent Ginzburg-Landau theory. In recent years, it has been realized that the presence of the extra fluid(s) can lead to astonishing and entirely unexpected new effects.By means of an ingenious, but rather controversial, mathematical argument, theoretical physicists Babaev, Faddeev and Niemi have argued that two-component Ginzburg-Landau theory can be reduced to an ostensibly entirely unrelated mathematical model called the Faddeev-Skyrme model. This would be extremely exciting, since the Faddeev-Skyrme model is known to possess so-called knot solitons: stable, localized lumps of energy which cannot dissipate since the field variable in which they reside is knotted in space. Quite apart from their intrinsic mathematical interest, the appearance of such knot solitons is unprecedented in condensed matter physics.The principal aim of the proposed reasearch is to answer definitively whether the Babaev-Faddeev-Niemi hypothesis is correct. The crux of their argument is to observe that when the direct coupling between certain of the fields in the two-component Ginzburg-Landau model is neglected (or turned off ) the model reduces to the Faddeev-Skyrme model. We will test this claim directly by simulating the behaviour of the Ginzburg-Landau model as the couplings are slowly turned back on. This will require large scale computer simulations on the White Rose parallel computation grid.