Broken Ergodicity in a Stochastic Model with Condensation

We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a pure high flow phase and a mixed phase, whereby the latter consists of a homogeneous high flow and a condensed low flow substate without translation invariance. The finite system alternates between these substates which both have diverging lifetimes in the thermodynamic limit, so ergodicity is broken in the infinite system. However, the scaling behaviour of the lifetimes in dependence of the system size is different due to different underlying flipping mechanisms.