  Cross-correlations are usually considered to emerge through interaction
between particles. Here we present a mechanism capable to generate power-law
cross-correlations between non-interacting particles exposed to an external
potential. This phenomenon can occur as an ensemble property when the external
potential induces intermittent dynamics, providing laminar and stochastic
phases of motion. We have strong indications that the divergence of the mean
residence time in the laminar phase of the single particle motion - sporadic
dynamics - is a sufficient condition for the emergence of long-range
cross-correlations. We argue that this mechanism may be relevant for the
occurrence of collective behaviour in critical systems.
