First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

Abstract

We consider a one-dimensional fluctuating interfacial profile governed by the Edwards-Wilkinson or the stochastic Mullins-Herring equation for periodic, standard Dirichlet and Dirichlet no-flux boundary conditions. The minimum action path of an interfacial fluctuation conditioned to reach a given maximum height $M$ at a finite (first-passage) time $T$ is calculated within the weak-noise approximation. Dynamic and static scaling functions for the profile shape are obtained in the transient and the equilibrium regime, i.e., for first-passage times $T$ smaller or lager than the characteristic relaxation time, respectively. In both regimes, the profile approaches the maximum height $M$ with a universal algebraic time dependence characterized solely by the dynamic exponent of the model. It is shown that, in the equilibrium regime, the spatial shape of the profile depends sensitively on boundary conditions and conservation laws, but it is essentially independent of them in the transient regime.

35 pages, 14 figures

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Cited by in corpus (4)

• Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry
• First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect
• Dynamics of the critical Casimir force for a conserved order parameter after a critical quench
• On the weak scaling of the contact distance between two fluctuating interfaces with system size