超导耦合使结孤子不稳定
Supercurrent coupling destabilizes knot solitons
摘要：
Babaev，Faddeev和Niemi在2002年发表的一篇有影响力的论文中指出，当复凝聚场对[psi_1，psi_2]：R^3 -> CP^1的投影等价类具有非零的Hopf度时，三维二分量Ginzburg-Landau（TCGL）理论应该支持结孤子。这个猜想是由TCGL模型的某种截断引起的，它将TCGL模型简化为Faddeev-Skyrme模型，该模型长期以来一直支持结孤子。在物理上，截断等于忽略了[psi_1，psi_2]与超流的耦合。本文通过数值跟踪结孤子来验证这种截断的有效性，发现当超导耦合重新打开时，结孤子会收缩并消失，从而得到真正的TCGL模型。这破坏了该猜想背后的推理，当与其他负面的数值研究相结合时，表明该猜想在其原始形式下不太可能是真的。
英文摘要：
In an influential paper of 2002, Babaev, Faddeev and Niemi conjectured that two-component Ginzburg-Landau (TCGL) theory in three dimensions should support knot solitons, where the projective equivalence class of the pair of complex condensate fields [psi_1,psi_2]:R^3 -> CP^1 has non-zero Hopf degree. The conjecture was motivated by a certain truncation of the TCGL model which reduced it to the Faddeev-Skyrme model, long known to support knot solitons. Physically, the truncation amounts to ignoring the coupling between [psi_1,psi_2] and the supercurrent of the condensates. The current paper presents a direct test of the validity of this truncation by numerically tracking the knot solitons as the supercurrent coupling is turned back on. It is found that the knot solitons shrink and disappear as the true TCGL model is reached. This undermines the reasoning underlying the conjecture and, when combined with other negative numerical studies, suggests the conjecture, in its original form, is very unlikely to be true.
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