Creation of defects with core condensation

Abstract

Defects in superfluid3 He, high-Tc superconductors, QCD colour superfluids and cosmic vortons can possess (anti)ferromagnetic cores, and their generalisations. In each case there is a second order parameter whose value is zero in the bulk which does not vanish in the core. We examine the production of defects in the simplest 1+1 dimensional scalar theory in which a second order parameter can take non-zero values in a defect core. We study in detail the effects of core condensation on the defect production mechanism.

Is domain formation decided before or after the transition?

“…Assuming that the final defect density is of the order of the inverse of the freeze-out correlation length, N def should scale as τ −σ Q . As discussed extensively in the literature and verified numerically for this model [17,18], the exponent is given by σ ≃ 1/4 in the dissipative regime, and σ ≃ 1/3 in the relativistic case.…”

“…We will consider a simple model in 1+1 dimensions that has been used as a first step in several studies of defect formation [17,18]. This model is easily amenable to numerical simulation and leads to the correct scaling laws for the defect density.…”

Experiments on spontaneous vortex formation in Josephson tunnel junctions

“…20 valid? To address the first problem of seeing how Eq. ͑3͒ can arise we are helped by the fact that, since the original KZ papers were published, there has been considerable analytic and numerical work performed for ideal systems obeying dissipative equations, 19,[29][30][31][32][33][34][35] in particular the time-dependent Ginzburg-Landau equation. Although there has been no attempt to model Josephson tunnel junctions we can draw several conclusions for JTJs from the phase transitions in simple systems, such as superfluids and superconductors, that suggests that small system size is not a problem in principle.…”

How Phase Transitions Induce Classical Behaviour

“…Hitherto, pure additive noise has been the basis for empirical stochastic equations in relativistic field theory that confirm Kibble's causal analysis [21]. However, recent numerical simulations with a more realistic mix of additive and multiplicative noise has shown that domain formation is unchanged [22].…”

“…If we adopt a single characteristic scale before then, ImδS now has two contributions. We have already seen that the first, of the form (22), but from the χ-loop, is sufficient to enforce decoherence before the transition is complete, for acceptable parameters. We also have a contribution of the form [10] …”