Universal coarsening of a two-dimensional Bose gas under conservative evolution

TL;DR

This study reveals universal phase ordering dynamics in a 2D Bose gas after a quench, showing temperature-dependent scaling laws and vortex-sound competition during coarsening.

Contribution

It demonstrates universal coarsening behavior in a 2D Bose gas across temperatures using the projected Gross-Pitaevskii equation, highlighting temperature-dependent dynamical critical exponents.

Findings

Scaling of correlation length as t^{1/z} with z varying with temperature

Temperature-dependent autocorrelation exponent λ diverging at zero temperature

Vortex and sound wave dynamics influence coarsening process

Abstract

We investigate the phase ordering dynamics of a uniform two-dimensional Bose gas quenched to a finite temperature in the superfluid phase. Starting from a defect-rich, far-from-equilibrium state, we model the subsequent evolution with the projected Gross-Pitaevskii equation, which conserves both energy and particle number. By tuning the initial energy, we control the effective post-quench temperature and examine its role in the equilibration dynamics. We find that the gas exhibits universal behaviour at all temperatures, evidenced by spatio-temporal scaling of correlation functions and power-law growth of the correlation length $\sim t^{1/z}$, with $z$ the dynamical critical exponent. We find $z$ to be temperature dependent, with $z \approx 1.5$ for post-quench temperatures just below the Berezinskii-Kosterlitz-Thouless (BKT) transition, and $z \approx 1.9$ for quenches to near-zero temperature. Analysis of the Porod tail of the momentum distribution suggests a temperature-dependent competition between vortices and sound waves in the coarsening process. The two-time correlation function also exhibits universal scaling, decaying as $\sim t^{-\lambda/z}$, with autocorrelation exponent $\lambda$. Near the BKT transition we obtain $\lambda \approx 2$, whereas $\lambda$ is found to diverge as the effective temperature approaches zero.