Non-Abelian Vortices in Condensed Matter Physics

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dc.creatorCho, Y. M.
dc.creatorKhim, Hyojoong
dc.creatorYong, Namsik
dc.date2003-08-11
dc.date2005-10-24
dc.date.accessioned2026-07-07T06:34:46Z
dc.date.available2026-07-07T06:34:46Z
dc.descriptionWe study the non-Abelian topological vortices in condensed matter physics, whose topological flux quantum number is described by $π_2(S^2)$, not by $π_1(S^1)$. We present two examples, a magnetic vortex in two-gap superconductor and a vorticity vortex in two-component Bose-Einstein condensate. In both cases the condensates exhibit a global SU(2) symmetry which allows the non-Abelian topology. We establish the non-Abelian flux quantization in two-gap superconductor by demonstrating the existence of non-Abelian magnetic vortex whose flux is quantized in the unit $4π/g$, not $2π/g$. We also discuss a genuine non-Abelian gauge theory of superconductivity which has a local SU(2) gauge symmetry, and establish the non-Abelian Meissner effect in the non-Abelian superconductor. We compare the non-Abelian vortices with the well-known Abelian Abrikosov vortex, and discuss how these non-Abelian vortices could be observed experimentally in two-gap superconductor made of ${\rm MgB_2}$ and spin-1/2 condensate of $^{87}{\rm Rb}$ atoms. Finally, we argue that the existence of the non-Abelian vortices provides a strong evidence for the existence of topological knots in these condensed matters whose topology is fixed by $π_3(S^2)$, which one can construct by twisting and connecting the periodic ends of the non-Abelian vortices.
dc.description17 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0308182
dc.identifierhttp://arxiv.org/abs/cond-mat/0308182
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99627
dc.subjectSuperconductivity
dc.subjectMathematical Physics
dc.subjectAtomic Physics
dc.titleNon-Abelian Vortices in Condensed Matter Physics
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