Abstract Rondoni: Slicer map and LÚvy-Lorentz gas: partial equivalence and nonequilibrium universality classes

The exactly solvable non-chaotic 1-dimensional Slicer Map (SM), that generates sub-, super-, and normal diffusion has neither expanding nor contracting regions. Like polygonal billiards, it preserves phase space volumes and its points separate only at discrete instants of time, when a "slicer" falls between, making their distance jump discontinuously. Analytical expressions for the moments and the position autocorrelations of this interval exchange transformation are derived and numerically compared to those predicted for the Levy-Lorentz gas. Fixing a single parameter, that allows the second moment of the SM to scale like the one of the Levy-Lorentz gas, all moments and two-points autocorrelation functions also agree. This allows an investigation of the properties of the Levy-Lorentz gas, which constitutes a hard open problem, even though the elementary dynamics of the two processes are totally different. This shows that even position-position correlation functions may not suffice to distinguish different anomalous transport processes in general. The existence of a kind of universality class for transport phenomena is envisaged.