Anomalous diffusion for a class of systems with two conserved quantities

Cedric Bernardin (1) , Gabriel Stoltz (2, 3)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 MICMAC - Methods and engineering of multiscale computing from atom to continuum

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. 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.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Cedric Bernardin, Gabriel Stoltz. Anomalous diffusion for a class of systems with two conserved quantities. Nonlinearity, 2012, 25, pp.1099-1133. ⟨10.1088/0951-7715/25/4/1099⟩. ⟨ensl-00909792⟩