 03156 Mustapha Mourragui, Enza Orlandi, Ellen Saada
 Macroscopic evolution of particle systems with random
field Kac interactions
(355K, Postscript)
Apr 4, 03

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We consider a lattice gas interacting via a Kac interaction
$J_\g(xy)$ of range $\g^{1}$, $\g>0$, $x,y\in\Z^d$ and under the
influence of an external random field given by independent bounded random
variables with a translation invariant distribution. We study the
evolution of the system through a conservative dynamics, i.e. particles
jump to nearest neighbor empty sites, with rates satisfying a detailed
balance condition with respect to the equilibrium measure. We prove
that rescaling space as $\g^{1}$ and time as $\g^{2}$, in the limit
$\g\to 0$, for dimension $d\ge 3$, the macroscopic density profile $\r$
satisfies, a.s. with respect to the random field, a nonlinear integral
differential equation, with a diffusion matrix determined by the
statistical properties of the external random field. The result holds
for all values of the density, also in the presence of phase segregation,
and the equation is in the form of the flux gradient for the energy
functional.
 Files:
03156.src(
03156.comments ,
03156.keywords ,
mostf.ps )