Two-dimensional particle motion in a random potential under ac bias

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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.