Boundary-induced heterogeneous absorbing states

TL;DR

This paper investigates how boundaries influence the formation of structured absorbing states in systems with many absorbing states, revealing different convergence behaviors depending on the presence of conservation laws and boundary types.

Contribution

It provides a comparative analysis of boundary effects on absorbing states in systems with and without conservation laws using mean-field and simulation methods.

Findings

Exponential convergence of background in directed percolation systems.

Power-law decay of landscapes in systems with conservation laws.

Structured backgrounds are noise-induced for reflecting walls.

Abstract

We study two different types of systems with many absorbing states (with and without a conservation law) and scrutinize the effect of walls/boundaries (either absorbing or reflecting) into them. In some cases, non-trivial structured absorbing configurations (characterized by a background field) develop around the wall. We study such structures using a mean-field approach as well as computer simulations. The main results are: i) for systems in the directed percolation class, a very fast (exponential) convergence of the background to its bulk value is observed; ii) for systems with a conservation law, power-law decaying landscapes are induced by both types of walls: while for absorbing walls this effect is already present in the mean-field approximation, for reflecting walls the structured background is a noise-induced effect. The landscapes are shown to converge to their asymptotic bulk values with an exponent equal to the inverse of the bulk correlation length exponent. Finally, the implications of these results in the context of self-organizing systems are discussed.