Anomalous diffusion for a class of systems with two conserved quantities
  We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. System of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows these models are still super-diffusive. This is proven rigorously for harmonic potentials. 
C\'edric Bernardin (UMPA-ENSL) and Gabriel Stoltz (CERMICS, Ecole des   Ponts and INRIA Rocquencourt)
cond-mat.stat-mech