  We investigate the transport properties of non-interacting particles
propagating in a finite Lorentz channel (LC). We show that interparticle
power-law correlations emerge, when the dynamics is described at a spatially
coarse-grained level. This behaviour appears in the non-equilibrium steady
state of the LC under flux boundary conditions and persists even in the
presence of external driving, provided that the billiard's horizon is infinite
in a static or temporal sense. We show that Fermi acceleration permits the
synchronization of particle motion with the periodic appearance of the
ballistic corridors, which, in turn, gives rise to intermittent dynamics and
the emergence of critical correlations. Thus, for the driven setup, the
critical state acts as an attractor possessing characteristics of
self-organization.
