Paolo Butta', Joel L. Lebowitz
Hydrodynamic Limit of Brownian Particles Interacting with Short and
Long Range Forces
(380K, PostScript)
ABSTRACT. We investigate the time evolution of a model system of interacting
particles, moving in a $d$-dimensional torus. The microscopic dynamics
are first order in time with velocities set equal to the negative
gradient of a potential energy term $\Psi$ plus independent Brownian
motions: $\Psi$ is the sum of pair potentials, $V(r)+\g^{d}J(\g r)$,
the second term has the form of a Kac potential with inverse range
$\g$. Using diffusive hydrodynamical scaling (spatial scale $\g^{-1}$,
temporal scale $\g^{-2}$) we obtain, in the limit $\g\downarrow 0$,
a diffusive type integro-differential equation describing the time
evolution of the macroscopic density profile.