Logarithmic superdiffusivity of the 2-dimensional anisotropic KPZ equation

TL;DR

This paper demonstrates that a two-dimensional anisotropic KPZ equation exhibits logarithmic superdiffusivity due to non-linear effects, contrasting previous beliefs of linear Edwards-Wilkinson scaling.

Contribution

The paper proves that non-linearity causes logarithmic superdiffusivity in the 2D anisotropic KPZ equation, challenging the traditional linear scaling assumption.

Findings

Non-linearity induces logarithmic superdiffusivity.

Contrasts with the folklore belief of Edwards-Wilkinson scaling.

Phenomenon similar to super-diffusivity in fluids and particle systems.

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.