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）彼此配对并开始表现得像流体时，超导性就发生了。在某些超导体中，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。这种情况在数学上由多组分金-朗道理论描述。近年来，人们意识到额外流体的存在会导致令人惊讶的、完全意想不到的新效应。通过一个巧妙的、但相当有争议的数学论证，理论物理学家巴巴耶夫、法捷耶夫和涅米认为，两组分金斯堡-朗道理论可以简化为一个表面上完全无关的数学模型，称为法捷耶夫-斯克尔姆模型。这将是非常令人兴奋的，因为Faddeev-Skyrme模型已知具有所谓的结孤子：稳定的，局部的能量块，由于它们所在的场变量在空间中打结，因此无法消散。这种结孤子的出现在凝聚态物理学中是前所未有的，其主要目的是明确回答Babaev-Faddeev-Niemi假设是否正确。他们的论点的关键是观察到，当忽略（或关闭）两分量金兹伯格-朗道模型中某些场之间的直接耦合时，该模型简化为法捷夫-斯克尔姆模型。我们将通过模拟Ginzburg-Landau模型的行为来直接验证这一说法，因为耦合是慢慢恢复的，这将需要在白色Rose并行计算网格上进行大规模的计算机模拟。

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.