Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in strongly coupled systems, in absence of quasiparticles, is especially challenging. We investigate breaking of U(1) symmetry and the resulting spontaneous formation of vortices in a (2 + 1)-dimensional holographic superconductor employing gauge/gravity duality, a ‘first-principles’ approach to study strongly coupled systems. Magnetic fluxons with quantized fluxes are seen emerging in the post-transition superconducting phase. As expected in type II superconductors, they are trapped in the cores of the order parameter vortices. The dependence of the density of these topological defects on the quench time, the dispersion of the typical winding numbers, and the vortex-vortex correlations are consistent with predictions of the Kibble-Zurek mechanism.
Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate universal signatures beyond the KZM, by characterizing the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor. The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the KZM and higher-order cumulants share the universal power-law scaling with the quench time. Extreme events associated with large fluctuations no longer exhibit a power-law behavior with the quench time and are characterized by a universal form of the Weibull distribution for different quench rates.
We studied the dynamics of the order parameter and the winding numbers W formation of a quenched normal-to-superconductor state phase transition in a finite size holographic superconducting ring. There is a critical circumference C below it no winding number will be formed, then C can be treated as the Kibble-Zurek mechanism (KZM) correlation length ξ which is proportional to the fourth root of its quench rate τQ, which is also the average size of independent pieces formed after a quench. When the circumference C ≥ 10ξ, the key KZM scaling between the average value of absolute winding number and the quench rate |W | ∝ τ −1/8 Q is observed. At smaller sizes, the universal scaling will be modified, there are two regions. The middle size 5ξagrees with a finite size experiment observation. While at ξ < C ≤ 5ξ the the average value of absolute winding number equals to the variance of winding number and there is no well exponential relationship between the quench rate and the average value of absolute winding number. The winding number statistics can be derived from a trinomial distribution with Ñ = C/(f ξ) trials, f 5 is the average number of adjacent pieces that are effectively correlated.
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