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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.

preprint2011arXivOpen access
Cédric BernardinGabriel Stoltz
cond-mat.stat-mech
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Cédric BernardinGabriel Stoltz

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