Knots and links in the order parameter distributions of strongly correlated systems
A.P. Protogenov
Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
Research on the coherent distribution of order parameters determining phase existence regions in the two-component Ginzburg-Landau model is reviewed. A major result of
this research, obtained by formulating this model in terms of
gauged order parameters (the unit vector field n, the density ρ2,
and the particle momentum c), is that some of the universal
phase and field configuration properties are determined by
topological features related to the Hopf invariant Q and its
generalizations. For sufficiently low densities, a ring-shaped
density distribution may be favored over stripes. For an L < Q
phase (L being the mutual linking index of the n and c field
configurations), a gain in free energy occurs when a transition to
a nonuniform current state occurs. A universal mechanism
accounting for decorrelation with increasing charge density is
discussed. The second part of the review is concerned with
implications of non-Abelian field theory for knotted configurations. The key properties of semiclassical configurations arising
in the Yang-Mills theory and the Skyrme model are discussed
in detail, and the relation of these configurations to knotted
distributions is scrutinized.
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