Boundary crossover in non-equilibrium growth processes

Abstract

The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near to the boundary than deep in the bulk. This is exemplified in the semi-infinite Edwards-Wilkinson model in one dimension, both from its exact solution and numerical simulations, as well as from simulations on the semi-infinite one-dimensional Kardar-Parisi-Zhang model. The non-stationary scaling of interface heights and widths is analyzed and a universal scaling form for the local height profile is proposed.

11 pages, 5 figures

References in corpus (3)

• An exact solution for the KPZ equation with flat initial conditions
• Directed polymer near a hard wall and KPZ equation in the half-space
• Glassy dynamics, aging and thermally activated avalanches in interface pinning at finite temperatures

Cited by in corpus (1)

• Surface growth on treelike lattices and the upper critical dimension of the KPZ class