Knots and links in the order parameter distributions of strongly correlated systems
Uzli i zatcepleniya raspredelenij parametrov poryadka v sil'no korrelirovannih sistemah

A.P. Protogenov
2006 Uspehi fiziceskih nauk  
Research on the coherent distribution of order parameters determining phase existence regions in the two-component Ginzburg ë Landau model is reviewed. A major result of this research ì obtained by formulating this model in terms of gauged order parameters (the unit vector éeld n, the density r 2 , and the particle momentum c) ì is that some of the universal phase and éeld conéguration properties are determined by topological features related to the Hopf invariant Q in its usual or generalized
more » ... orm. For suféciently low densities, a ring-shaped density distribution may be favored over stripes. For a L 'Q phase (L being the mutual linking index of the n and c éeld conégurations) a gain in free energy occurs when a transition to an nonuniform current state takes place. A universal mechanism accounting for decorrelation with increasing charge density is discussed. The second part of the review is concerned with what non-Abelian éeld theory has to say on the topic of knotted conégurations. The key properties of quasi-classical conégurations arising in Yang ë Mills theory and the Skyrme model are discussed in detail, and the relation of these conégurations to knotted distributions is scrutinized.
doi:10.3367/ufnr.0176.200607a.0689 fatcat:bvdfdofodjbyldojfypxgltlci