Crossover in the dynamical critical exponent of a quenched two-dimensional Bose gas

TL;DR

This paper investigates the phase ordering dynamics of a 2D Bose gas after a quench, revealing a crossover in the dynamical critical exponent from dissipative to conservative regimes, influenced by vortex-sound interactions.

Contribution

It provides the first numerical evidence of a smooth crossover in the dynamical critical exponent in a quenched 2D Bose gas, highlighting the role of vortex mobility.

Findings

Universal scaling observed regardless of dissipation strength.

Growth law transitions from logarithmic correction to power-law as dissipation decreases.

Anomalous lower exponent linked to vortex-sound interactions.

Abstract

We study the phase ordering dynamics of a uniform Bose gas in two dimensions following a quench into the ordered phase. We explore the crossover between dissipative and conservative evolution by performing numerical simulations within the classical field methodology. Regardless of the dissipation strength, we find clear evidence for universal scaling, with dynamical critical exponent $z$ characterising the growth of the correlation length. In the dissipative limit we find growth consistent with the logarithmically corrected law $[t/\log(t/t_0)]^{1/z}$, and exponent $z=2$, in agreement with previous studies. Decreasing the dissipation towards the conservative limit, we find strong numerical evidence for the expected growth law $t^{1/z}$. However, we observe a smooth crossover in $z$ that converges to an anomalous value distinctly lower than $2$ at a small finite dissipation strength. We show that this lower exponent may be attributable to a power-law vortex mobility arising from vortex--sound interactions.