Nils Berglund (CPT-Toulon)

Metastability and synchronization in a noisy classical chain.

Joint work with Bastien Fernandez (CPT-Marseille) and Barbara Gentz (WIAS, Berlin)

We consider a chain of N overdamped bistable oscillators with nearest-neighbour coupling. Each site is perturbed by an independent white noise, modeling the influence of a heat reservoir. The system is described by a set of stochastic differential equations on R^(Z/NZ). The metastable behaviour of the dynamics is encoded in the potential landscape, in particular its local minima and saddles of index 1. At small coupling, the system has 2^N local minima, while at sufficiently large coupling (of the order N^2), it synchronises: There are only two local minima, corresponding to all particles in the same state. We show that as the coupling decreases, the system desynchronises in a sequence of symmetry-breaking bifurcations, which gradually increase the number of local minima from 2 to 2^N. We provide precise estimates on the activation energy and optimal transition paths and times from one synchronised state to the other, in particular in the large-N limit.