Vortex Dynamics in a Compact Kardar-Parisi-Zhang System

Abstract

We study the dynamics of vortices in a two-dimensional, nonequilibrium system, described by the compact Kardar-Parisi-Zhang equation, after a sudden quench across the critical region. Our exact numerical solution of the phase-ordering kinetics shows that the unique interplay between nonequilibrium and the variable degree of spatial anisotropy leads to different critical regimes. We provide an analytical expression for the vortex evolution, based on scaling arguments, which is in agreement with the numerical results, and confirms the form of the interaction potential between vortices in this system.

Searching for the Kardar-Parisi-Zhang phase in microcavity polaritons

“…Furthermore, the distribution of the signal's phase fluctuations also match the universal form expected in the stationary limit for the 2D KPZ class. We also prove using different initial conditions that the steady state of the system does not contain any vortices, in stark contrast to what has been seen in the isotropic compact KPZ equation [25] and expected in incoherently driven systems [16]. The dramatic change in the form of spatial correlations seen when the pump strength is tuned to within the window where KPZ behavior is expected at all length scales suggests that this regime should be easy to distinguish despite the small range of pump strengths for which it occurs.…”

“…Compared to the phase equation for thermal equilibrium condensates, the KPZ equation has additional nonlinear terms arising from the drive and dissipation, which cause correlations to take a more rapidly decaying form [12]. In addition to potentially providing another much sought after experimental platform for investigating the 2D KPZ universality class, the phase being a compact variable offers a window into interesting new physics regarding the dynamics of vortices in the phase governed by the KPZ equation [16,17,[24][25][26].…”

Emergent Kardar-Parisi-Zhang phase in quadratically driven condensates

“…(6), we find that complex fields are short-range correlated via a stretched exponential, leading to the conclusion that no phase transition can take place. Whether the ordered phase is completely removed, or survives for large values of the two-particle drive (corresponding to large values of g) cannot be determined from our analysis, as the RG analysis is not valid for non-perturbative values of g. Finally, here we neglected the presence of topological excitations, such as vortices and anti-vortices, which are essential to describe the transition between the KPZ and a normal, featureless phase [53][54][55][56][57][58]. The impact of the Z 2 symmetry on these excitations is left for future work.…”