Langevin equations coupled through correlated noises

We consider the dynamics of non-interacting Brownian particles which are dr iven by correlated (non-independent) noise sources. In simple confining pot entials the particles tend to aggregate as the noise correlation is increas ed. If two particles are subject to the same noise they will coalesce and r emain together ever after. We show that complete aggregation of the particl es can be expected even in the case of a disordered potential which does no t coniine the individual particle trajectories. Finally, we examine the cas e of correlation in the noises which depends on the separation of the two p articles.