Kardar-Parisi-Zhang equation with short-range correlated noise: Emergent symmetries and nonuniversal observables - Archive ouverte HAL Access content directly
Journal Articles Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Year : 2017

Kardar-Parisi-Zhang equation with short-range correlated noise: Emergent symmetries and nonuniversal observables

Abstract

We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the Kardar-Parisi-Zhang (KPZ) dynamics with a noise featuring smooth spatial correlations of characteristic range ξ. We employ nonperturbative functional renormalization group methods to resolve the properties of the system at all scales. We show that the physics of the standard (uncorrelated) KPZ equation emerges on large scales independently of ξ. Moreover, the renormalization group flow is followed from the initial condition to the fixed point, that is, from the microscopic dynamics to the large-distance properties. This provides access to the small-scale features (and their dependence on the details of the noise correlations) as well as to the universal large-scale physics. In particular, we compute the kinetic energy spectrum of the stationary state as well as its nonuniversal amplitude. The latter is experimentally accessible by measurements at large scales and retains a signature of the microscopic noise correlations. Our results are compared to previous analytical and numerical results from independent approaches. They are in agreement with direct numerical simulations for the kinetic energy spectrum as well as with the prediction, obtained with the replica trick by Gaussian variational method, of a crossover in ξ of the nonuniversal amplitude of this spectrum.
Fichier principal
Vignette du fichier
pre_95_032117.pdf (963.1 Ko) Télécharger le fichier
Origin Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01555188 , version 1 (02-03-2018)

Identifiers

Cite

Steven Mathey, Elisabeth Agoritsas, Thomas Kloss, Vivien Lecomte, Léonie Canet. Kardar-Parisi-Zhang equation with short-range correlated noise: Emergent symmetries and nonuniversal observables. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2017, 95 (3), pp.032117. ⟨10.1103/PhysRevE.95.032117⟩. ⟨hal-01555188⟩
621 View
184 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More