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Gauge turbulence, topological defect dynamics, and condensation in Higgs models

The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such systems equilibrating after a strong initial quench such as the overpopulation of the infrared modes. While the final equilibrium state does not support confinement, metastable vortex defect configurations appear in the gauge field which are found to be closely related to the appearance of physically observable confined electric and magnetic charges. These phenomena are seen to be intimately related to the approach of a non-thermal fixed point of the far-from-equilibrium dynamical evolution, signalled by universal scaling in the gauge-invariant correlation function of the Higgs field. Even when the parameters of the Higgs action do not support condensate formation in the vacuum, during this approach, transient Higgs condensation is observed. We discuss implications of these results for the far-from-equilibrium dynamics of Yang-Mills fields and potential mechanisms how confinement and condensation in non-abelian gauge fields can be understood in terms of the dynamics of Higgs models. These suggest that there is an interesting new class of dynamics of strong coherent turbulent gauge fields with condensates.