Anomalous diffusion for a class of systems with two conserved quantities

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.

References in corpus (6)

• Heat Transport in low-dimensional systems
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Local Temperature and Universal Heat Conduction in FPU chains
• Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities
• Thermal conductivity of the Toda lattice with conservative noise
• Strong Feller Continuity of Feller Processes and Semigroups

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