Stationary State Skewness in KPZ Type Growth

TL;DR

This paper investigates the skewness of stationary states in KPZ type growth models, revealing that these states are typically skewed, lack particle-hole symmetry, and that skewness diverges with system size, but is irrelevant at the KPZ fixed point.

Contribution

It constructs the exact stationary state for the 1+1D RSOS model, analyzes skewness behavior, and shows that KPZ fixed point has zero skewness, advancing understanding of non-equilibrium surface growth.

Findings

Stationary states are typically skewed and asymmetric.

Skewness diverges with system size but is irrelevant at the KPZ fixed point.

Exact stationary state constructed for the 1+1D RSOS model.

Abstract

Stationary states in KPZ type growth have interesting short distance properties. We find that typically they are skewed and lack particle-hole symmetry. E.g., hill-tops are typically flatter than valley bottoms, and all odd moments of the height distribution function are non-zero. Stationary state skewness can be turned on and off in the 1+1 dimensional RSOS model. We construct the exact stationary state for its master equation in a 4 dimensional parameter space. In this state steps are completely uncorrelated. Familiar models such as the Kim-Kosterlitz model lie outside this space, and their stationary states are skewed. We demonstrate using finite size scaling that the skewness diverges with systems size, but such that the skewness operator is irrelevant in 1+1 dimensions, with an exponent $y_{sk}\simeq-1$, and that the KPZ fixed point lies at zero-skewness.