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Register a new userTime dependent couplings and crossover length scales in non-equilibrium surface roughening
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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.
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We present a modified version of the one-dimensional sine-Gordon that exhibits a thermodynamic, roughening phase transition, in analogy with the 2D usual sine-Gordon model. The model is suited to study the crystalline growth over an impenetrable substrate and to describe the wetting transition of a liquid that forms layers. We use the transfer integral technique to write down the pseudo-Schrodinger equation for the model, which allows to obtain some analytical insight, and to compute numerically the free energy from the exact transfer operator. We compare the results with Monte Carlo simulations of the model, finding a perfect agreement between both procedures. We thus establish that the model shows a phase transition between a low temperature flat phase and a high temperature rough one. The fact that the model is one dimensional and that it has a true phase transition makes it an ideal framework for further studies of roughening phase transitions.
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We study numerically the roughening properties of an interface in a two-dimensional Ising model with either random bonds or random fields, which are representative of universality classes where disorder acts only on the interface or also away from it, in the bulk. The dynamical structure factor shows a rich crossover pattern from the form of a pure system at large wavevectors $k$, to a different behavior, typical of the kind of disorder, at smaller $k$s. For the random field model a second crossover is observed from the typical behavior of a system where disorder is only effective on the surface, as the random bond model, to the truly large scale behavior, where bulk-disorder is important, that is observed at the smallest wavevectors.
While studying systems driven out of equilibrium, one usually employs a drive that is not directly coupled to the degrees of freedom of the system. In contrast to such a case, we here unveil a hitherto unexplored situation of state-dependent driving, whereby a direct coupling exists between the two. We demonstrate the ubiquity of such a driving, and establish that it leads to a nontrivial steady-state that is qualitatively opposite to what is observed in other driven systems. Further, we show how state-dependent driving in a many-body system can be effectively captured in terms of a single-particle model. The origin of this description may ultimately be traced to the fact that state-dependent driving results in a force that undergoes repeated resetting in time.
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