The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application Fermi acceleration induces self-organized critical characteristics to the driven

The Lorentz gas (LG) acts in the theory of dynamical systems as a paradigm allowing us to address fundamental issues of statistical mechanics, for instance, transport processes, such as diffusion in the configuration space [1, 2]. The static periodic LG comprises a regular lattice of circular fixed scat-terers and an ensemble of non-interacting particles travelling freely between collisions and scattering elastically off the circular obstacles. The transport properties of such a system are determined by the billiard’s geometry, that is the specific lattice symmetry and the lattice constant. If the maximum free path length is not bounded from above, then the setup possesses a so-called infinite horizon (IH) and the diffusion in configuration space is anomalous [4, 5]. For a more compact packing of the scatterers, i.e. finite horizon (FH), arbitrarily long flights are not possible and the system exhibits normal diffusion. Time-dependent generalizations of the original periodic Lorentz gas model have been introduced, in which the scatterers are allowed to oscillate [6, 8], rendering the study of diffusion in momentum space possible. This process is intimately linked to Fermi acceleration [3], which is considered a fundamental acceleration mechanism in many areas of physics. The mechanism consists in the indefinite increase of the mean energy of particles as a result of random collisions with moving scatterers. In this work [9], we show the emergence of power-law (critical) cross-correlations betwee