Logarithmic superdiffusivity of the 2-dimensional anisotropic KPZ equation
Statistical Mechanics
2020-09-29 v1 Disordered Systems and Neural Networks
Mathematical Physics
math.MP
Abstract
We study an anisotropic variant of the two-dimensional Kardar-Parisi-Zhang equation, that is relevant to describe growth of vicinal surfaces and has Gaussian, logarithmically rough, stationary states. While the folklore belief (based on one-loop Renormalization Group) is that the equation has the same scaling behaviour as the (linear) Edwards-Wilkinson equation, we prove that, on the contrary, the non-linearity induces the emergence of a logarithmic super-diffusivity. This phenomenon is similar in flavour to the super-diffusivity for two-dimensional fluids and driven particle systems.
Cite
@article{arxiv.2009.12934,
title = {Logarithmic superdiffusivity of the 2-dimensional anisotropic KPZ equation},
author = {Giuseppe Cannizzaro and Dirk Erhard and Fabio Toninelli},
journal= {arXiv preprint arXiv:2009.12934},
year = {2020}
}
Comments
5 pages