Anomalous diffusion for a class of systems with two conserved quantities (Q2882659)

The authors consider a class of one dimensional deterministic models of energy volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. They then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. A system of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows that these models are still super-diffusive. This is proven rigorously for harmonic potentials. This is very interesting work.