Logarithmic or algebraic: roughening of an active Kardar-Parisi-Zhang surface

TL;DR

This paper extends the KPZ equation by adding a nonlocal nonlinear term, revealing new regimes of interface roughness, including sublogarithmic and superlogarithmic behaviors, with implications for nonlocal surface growth models.

Contribution

It introduces a generalized active KPZ equation with a nonlocal nonlinear term, exploring stability and roughness regimes, which broadens understanding of nonlocal surface growth phenomena.

Findings

Stable regimes exhibit sublogarithmic or superlogarithmic roughness.

Unstable regimes suggest algebraic roughness or short-range order.

Model serves as a paradigmatic nonlocal growth equation.

Abstract

The Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including a symmetry-permitted nonlocal nonlinear term of active origin that is of the same order as the one included in the KPZ equation. Including this term, the 2D active KPZ equation is stable in some parameter regimes, in which the interface conformation fluctuations exhibit sublogarithmic or superlogarithmic roughness, with nonuniversal exponents, giving positional generalised quasi-long-ranged order. For other parameter choices, the model is unstable, suggesting a perturbatively inaccessible algebraically rough interface or positional short-ranged order. Our model should serve as a paradigmatic nonlocal growth equation.