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arXiv · 1105.2618

Anomalous diffusion for a class of systems with two conserved quantities

Cédric Bernardin·Gabriel Stoltz
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Abstract

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.

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Cédric Bernardin, Gabriel Stoltz. 2011-12-02. Anomalous diffusion for a class of systems with two conserved quantities. https://doi.org/10.1088/0951-7715%2F25%2F4%2F1099

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