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.