Universal statistics of vortices in a newborn holographic superconductor: beyond the Kibble-Zurek mechanism

Abstract

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.

Distribution of Kinks in an Ising Ferromagnet After Annealing and the Generalized Kibble-Zurek Mechanism

“…Indeed, a framework to account for the distribution of topological defects generated across a classical continuous phase transition has been put forward and predicts a binomial distribution, in agreement with numerical simulations for the timedependent Ginzburg-Landau theory [45]. In higher dimensional systems, further evidence for the presence of universality in the full counting statistics of topological defects has been provided by the study of the vortex number distribution in a newborn holographic superconductor, which was predicted to be Poissonian [46]. At the time of writing, experimental evidence of Poissonian vortex statistics has been reported after cooling of an atomic Bose gas into a superfluid in finite time [47].…”

“…A growing body of results [41][42][43][44][45][46] suggests that the signatures of universality govern the kink number distribution and not only its mean value. To appreciate this, in a classical setting, it suffices to assume that the formation of kinks at different locations is described by independent stochastic events [45].…”

Exact thermal properties of free-fermionic spin chains

“…These results have also been extended to nonlinear quenches [17,18] and inhomogeneous systems [19][20][21][22][23], while their breakdown has been characterized in open systems [24][25][26]. More recently, it has been shown that signatures of universality are present in the full kink-number distribution and that all cumulants scale as a universal power-law of the quench time [16,[27][28][29][30][31]. The universal dynamics of defect formation is not always desirable, and a variety of works have been devoted to circumvent it using diverse control protocols [32][33][34][35][36][37][38][39][40][41][42], beyond the use of nonlinear quenches and inhomogeneous driving.…”

Exact thermal properties of free-fermionic spin chains

“…These results have also been extended to nonlinear quenches [16,17] and inhomogeneous systems [18][19][20][21][22], while their breakdown has been characterized in open systems [23][24][25]. More recently, it has been shown that signatures of universality are present in the full kink-number distribution and that all cumulants scale as a universal power-law of the quench time [15,[26][27][28][29][30]. The universal dynamics of defect formation is not always desirable, and a variety of works have been devoted to circumvent it using diverse control protocols [31][32][33][34][35][36][37][38][39][40][41], beyond the use of nonlinear quenches and inhomogeneous driving.…”