Figure 1

Half-width of the averaged two-point correlation function (13) during the quench: ${\xi }_{1/2}$. (a) and (b): ${\xi }_{1/2}$ before and after rescalings. On both plots black, red (dark gray), and green (light gray) lines correspond to ${\tau }_Q=5$, 25 and 85, respectively. The inset magnifies the region where the KZM works best. (c) Illustration that quench imprints a characteristic length scale $\widehat{\xi }\sim {\tau }_Q^{\nu /(1+z\nu )}={\tau }_Q^{1/4}$ (7). We study ${\xi }_{1/2}$ at the critical point. The scale is logarithmic on both axes: circles show numerics, while the straight line is a fit to numerics: $\ln {\xi }_{1/2}(\epsilon =0)=-1.53\pm 0.03+(0.24\pm 0.01)\ln {\tau }_Q$. The fit confirms the predicted $1/4$ exponent. (d) Illustration that quench imprints a characteristic time scale $\widehat{t}\sim {\tau }_Q^{z\nu /(1+z\nu )}={\tau }_Q^{1/2}$. We study time $\Delta t$ passing from entering the broken-symmetry phase to the moment when ${\xi }_{1/2}/\widehat{\xi }$ reaches a threshold, assumed here to be 0.5, i.e., to be near the center of the region where rescalings work on the broken-symmetry side [see inset of (b)]. The scale is logarithmic on both axes: circles show numerics, while straight line is a fit to numerics: $\ln \Delta t=2.60\pm 0.04+(0.49\pm 0.01)\ln {\tau }_Q$. This is in good agreement with theoretical prediction of $\Delta t\sim {\tau }_Q^{1/2}$. We use for this plot $\widehat{\xi }$ taken from the fit done in plot (c): $\widehat{\xi }={\tau }_Q^{0.24}$. Fits from plots (c) and (d) allow for measurement of $z$ and $\nu$ critical exponents. The results present averages over 100 runs with different noise. See 17 for other parameters.Reuse & Permissions

Figure 2

Snapshot of density $|\varphi (x){|}^2$, phase $\arg (\varphi )$, and gradient of phase $\frac{d}{dx}\arg (\varphi )$ (the velocity field). The snapshot is taken for one evolution (no averaging) at $\epsilon (t)=10$ for ${\tau }_Q=10$. See 17 for other parameters.Reuse & Permissions

Figure 3

Number of solitons in the broken-symmetry phase before and after rescalings. On both plots black, red (dark gray), and green (light gray) lines correspond to ${\tau }_Q=10$, 40 and 70, respectively. The inset magnifies the region where KZM works best. The results present averages over 100 runs with different noise. See 17 for other parameters.Reuse & Permissions