Effect of random environment on kinetic roughening: Kardar-Parisi-Zhang model with a static noise coupled to the Navier-Stokes equation

TL;DR

This paper investigates how a randomly moving medium influences the kinetic roughening of surfaces modeled by the KPZ equation with static noise, using a field-theoretic renormalization group approach.

Contribution

It extends the KPZ model to include a stochastic Navier-Stokes medium, introducing new nonlinearities and parameters, and analyzes the resulting fixed points via renormalization group methods.

Findings

Identification of a renormalizable action functional with four couplings

Discovery of a fixed point curve with an infrared attractive segment for positive epsilon

Extension of the KPZ model to coupled scalar and velocity fields

Abstract

Kinetic roughening of a randomly growing surface can be modelled by the Kardar-Parisi-Zhang equation with a time-independent (``spatially quenched'' or ``columnar'') random noise. In this paper, we use the field-theoretic renormalization group approach to investigate how randomly moving medium affects the kinetic roughening. The medium is described by the stochastic differential Navier-Stokes equation for incompressible viscous fluid with an external stirring force. We find that the action functional for the full stochastic problem should be extended to be renormalizable: a new nonlinearity must be introduced. Moreover, in order to correctly couple the scalar and velocity fields, a new dimensionless parameter must be introduced as a factor in the covariant derivative of the scalar field. The resulting action functional involves four coupling constants and a dimensionless ratio of kinematic coefficients. The one-loop calculation (the leading order of the expansion in $\varepsilon=4-d$ with $d$ being the space dimension) shows that the renormalization group equations in the five-dimensional space of those parameters reveal a curve of fixed points that involves an infrared attractive segment for $\varepsilon>0$.