Defect Formation and Local Gauge Invariance

Abstract

We propose a new mechanism for formation of topological defects in a U(1) model with a local gauge symmetry. This mechanism leads to definite predictions, which are qualitatively different from those of the Kibble-Zurek mechanism of global theories. We confirm these predictions in numerical simulations, and they can also be tested in superconductor experiments. We believe that the mechanism generalizes to more complicated theories.

Defect Formation in Superconducting Rings: External Fields and Finite-Size Effects

“…This allows us to test different ring geometries (the KZ picture implies only perimeter scaling behaviour, indifferent to ring shape and width), and the breakdown of the KZ scaling laws for small systems. In addition, with dynamic electromagnetic fields, we can determine the likelihood of observing HindmarshRajantie magnetic field freeze-out 11 , which also goes beyond the KZ scenario.…”

Symmetry Breaking and Defects

“…There is some doubt about how to compute the number of defects formed in a transition in a theory with a local gauge symmetry. There is another mechanism operating in a gauge theory [46,52], but if anything this makes the discrepancy more puzzling because it tends to suggest that the Zurek prediction of defect numbers would be an underestimate. On the other hand, it is worth noting that the inequality (114) is also seriously violated in the superconducting film experiment, though whether the argument leading to it is valid in the case of symmetry breaking in a gauge theory is not clear.…”

Design of magneto-optical system for imaging of magnetic flux created during a conductor–superconductor phase transition

“…There is no correlation between topological defects in vertices that are not nearest neighbours (P(n v1 Z1;n v3 Z1)ZP(n v1 Z1; n v3 ZK1)ZP(n v1 Z1)P(n v3 Z1)Z1/64), and therefore there are no long-range correlations. Another mechanism of vortex creation in superconductor is a fluxtrapping mechanism proposed by Hindmarsh & Rajantie (2000); see also Kibble & Rajantie (2003). In this mechanism, the flux is generated by fluctuations of the magnetic field, which become frozen out during the quench.…”

“…In the gauge theory, vortex-vortex correlations at short distances are expected. The vortices should be formed in clusters of equal sign (Hindmarsh & Rajantie 2000;Kibble & Rajantie 2003). After the transition, topological defects with opposite polarity that are close to one another will annihilate rapidly.…”

“…In this mechanism, the flux is generated by fluctuations of the magnetic field, which become frozen out during the quench. The two mechanisms (Kibble 1976;Hindmarsh & Rajantie 2000) predict a distribution of defects with characteristically different correlation properties. In the gauge theory, vortex-vortex correlations at short distances are expected.…”