Abstract Rondoni: Slicer map and Lévy-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.