  We study the influence of particle interaction on a quantum walk on a
bipartite one-dimensional lattice with decay from every second site. The
corresponding non-interacting (linear) system has been shown to have a
topological transition described by the average displacement before decay. Here
we use this topological quantity to distinguish coherent quantum dynamics from
incoherent classical dynamics caused by a breaking of the translational
symmetry. We furthermore analyze the behavior by means of a rate equation
providing a quantitative description of the incoherent nonlinear dynamics.
