One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems

Abstract

While the 1-point height distributions (HDs) and 2-point covariances of $(2+1)$ KPZ systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and nothing is known about the spatial and temporal covariances. Here, we report results for these quantities, obtained from extensive numerical simulations of discrete KPZ models, for three different setups yielding cylindrical growth. Beyond demonstrating the universality of the HD and covariances, our results reveal other interesting features of this geometry. For example, the spatial covariances measured along the longitudinal and azimuthal directions are different, with the former being quite similar to the curve for flat $(2+1)$ KPZ systems, while the latter resembles the Airy${}_2$ covariance of circular $(1+1)$ KPZ interfaces. We also argue (and present numerical evidence) that, in general, the rescaled temporal covariance $\mathcal{A}(t/t_0)$ decays asymptotically as $\mathcal{A}(x)\sim x^{-\bar{\lambda }}$ with an exponent $\bar{\lambda }=\beta +d^{\ast }/z$, where $d^{\ast }$ is the number of interface sides kept fixed during the growth (being $d^{\ast }=1$ for the systems analyzed here). Overall, these results complete the picture of the main statistics for the $(2+1)$ KPZ class.

10 pages, 8 figures, 2 tables

References in corpus (15)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Growing interfaces uncover universal fluctuations behind scale invariance
• An exact solution for the KPZ equation with flat initial conditions
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Slow relaxation and aging kinetics for the driven lattice gas
• Interface fluctuations for deposition on enlarging flat substrates
• Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition
• Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth
• On the origins of scaling corrections in ballistic growth models
• Random geometry and the Kardar-Parisi-Zhang universality class
• Kardar-Parisi-Zhang universality class in ($d+1$)-dimensions
• Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time

Cited by in corpus (1)

• Dimensional crossover in Kardar-Parisi-Zhang growth