Quantifying Nonequilibrium Behavior with Varying Cooling Rates

Abstract

We investigate nonequilibrium behavior in (1+1)-dimensional stochastic field theories in the context of Ginzburg-Landau models at varying cooling rates. We argue that a reliable measure of the departure from thermal equilibrium can be obtained from the absolute value of the rate of change of the momentum-integrated structure function, $\Delta S_{\mathrm{tot}}$. We show that the peak of $\Delta S_{\mathrm{tot}}$ scales with the cooling, or quench, time-scale, ${\tau }_q$, in agreement with the prediction by Laguna and Zurek for the scaling of freeze-out time in both over and under-damped regimes. Furthermore, we show that the amplitude of the peak scales as ${\tau }_q^{-6/5}$ independent of the viscosity.

Comments: 4 pages, 4 figures, submitted to Phys. Rev. Lett