Superdiffusivity of Two Dimensional Lattice Gas Models

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Superdiffusivity of Two Dimensional Lattice Gas Models

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Title: Superdiffusivity of Two Dimensional Lattice Gas Models
Author: Landim, Claudio; Ramírez, José A.; Yau, Horng-Tzer

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Citation: Landim, Claudio, José A. Ramírez, and Horng-Tzer Yau. 2005. “Superdiffusivity of Two Dimensional Lattice Gas Models.” Journal of Statistical Physics 119 (5-6) (June): 963–995. doi:10.1007/s10955-005-4297-1.
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Abstract: It was proved [Navier–Stokes Equations for Stochastic Particle System on the Lattice. Comm. Math. Phys. (1996) 182, 395; Lattice gases, large deviations, and the incompressible Navier–Stokes equations. Ann. Math. (1998) 148, 51] that stochastic lattice gas dynamics converge to the Navier–Stokes equations in dimension d=3 in the incompressible limits. In particular, the viscosity is finite. We proved that, on the other hand, the viscosity for a two dimensional lattice gas model diverges faster than (log t)1/2. Our argument indicates that the correct divergence rate is (log t)1/2. This problem is closely related to the logarithmic correction of the time decay rate for the velocity auto-correlation function of a tagged particle.
Published Version: doi:10.1007/s10955-005-4297-1
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