Hidden symmetry and knot solitons in a charged two-condensate Bose system

Abstract

We show that a charged two-condensate Ginzburg-Landau model or equivalently a Gross-Pitaevskii functional for two charged Bose condensates, can be mapped onto a version of the nonlinear O(3) $\sigma$-model. This implies in particular that such a system possesses a hidden O(3) symmetry and allows for the formation of stable knotted solitons. The results, in particular, should be relevant to the superconducting MgB_2.

This version will appear in Phys. Rev. B, added a comment on the case when condensates in two bands do not independently conserve, also added a figure and references to experimental papers on MgB_2 (for which our study is relevant). Miscellaneous links on knot solitons are also available at the homepage of one of the authors http://www.teorfys.uu.se/PEOPLE/egor/ . Animations of knot solitons are available at http://users.utu.fi/h/hietarin/knots/c45_p2.mpg

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• Beyond Eliashberg superconductivity in MgB2: anharmonicity, two-phonon scattering, and multiple gaps
• Evidence for two superconducting energy gaps in MgB2 by point-contact spectroscopy
• Specific Heat of Mg ^{11}B_2
• Aspects of Electric and Magnetic Variables in SU(2) Yang-Mills Theory
• QCD versus Skyrme-Faddeev Theory
• Faddeev-Niemi Conjecture and Effective Action of QCD

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