Time dependent couplings and crossover length scales in non-equilibrium surface roughening

TL;DR

This paper investigates how time-dependent couplings influence the scaling behavior of surface roughening in non-equilibrium models, revealing complex crossover phenomena and providing insights into spontaneous imbibition.

Contribution

It introduces the role of time-dependent couplings in non-equilibrium surface roughening, showing their impact on scaling properties and crossover behaviors.

Findings

Time-dependent couplings can cause anomalous scaling above crossover lengths.

Crossover lengths can produce rough surfaces even when flattening terms dominate.

Analysis clarifies the role of time-dependent couplings in spontaneous imbibition.

Abstract

We show that time dependent couplings may lead to nontrivial scaling properties of the surface fluctuations of the asymptotic regime in non-equilibrium kinetic roughening models . Three typical situations are studied. In the case of a crossover between two different rough regimes, the time-dependent coupling may result in anomalous scaling for scales above the crossover length. In a different setting, for a crossover from a rough to either a flat or damping regime, the time dependent crossover length may conspire to produce a rough surface, despite the most relevant term tends to flatten the surface. In addition, our analysis sheds light into an existing debate in the problem of spontaneous imbibition, where time dependent couplings naturally arise in theoretical models and experiments.