The inviscid fixed point of the multi-dimensional Burgers-KPZ equation

TL;DR

This paper investigates the inviscid fixed point of the multi-dimensional Burgers-KPZ equation, revealing its existence across all dimensions and its role in controlling large momentum behavior with a super-universal dynamical exponent of z=1.

Contribution

The study extends the understanding of the inviscid Burgers-KPZ fixed point from one dimension to higher dimensions using functional renormalization group analysis.

Findings

The IB fixed point exists in all dimensions d ≥ 0.

It controls the large momentum behavior of correlation functions.

It predicts a super-universal dynamical exponent z=1 in all dimensions.

Abstract

A new scaling regime characterized by a $z=1$ dynamical critical exponent has been reported in several numerical simulations of the one-dimensional Kardar-Parisi-Zhang and noisy Burgers equations. In these works, this scaling, differing from the well-known KPZ one $z=3/2$, was found to emerge in the tensionless limit for the interface and in the inviscid limit for the fluid. Based on functional renormalization group, the origin of this scaling has been elucidated. It was shown to be controlled by a yet unpredicted fixed point of the one-dimensional Burgers-KPZ equation, termed inviscid Burgers (IB) fixed point. The associated universal properties, including the scaling function, were calculated. All these findings were restricted to $d=1$, and it raises the intriguing question of the fate of this new IB fixed point in higher dimensions. In this work, we address this issue and analyze the multi-dimensional Burgers-KPZ equation using functional renormalization group. We show that the IB fixed point exists in all dimensions $d\geq 0$, and that it controls the large momentum behavior of the correlation functions in the inviscid limit. It turns out that it yields in all $d$ the same super-universal value $z=1$ for the dynamical exponent.