  We study the Brownian motion of a single particle coupled to an external ac
field in a two-dimensional random potential. We find that for small fields a
large-scale vorticity pattern of the steady-state net currents emerges, a
consequence of local symmetry breaking. In this regime the net currents are
highly correlated, the spatial correlation function follows a logarithmic
dependence, and the correlation length is of the order of the system size. For
large external fields correlations disappear and only random net currents
patterns are observed. The numerical analysis indicates that the correlation
length scales as a power law with both the size of the system and the amplitude
of the ac field.
