Critical non-equilibrium steady states of the Lorentz channel

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.