On homogenization of a diffusion perturbed by a periodic reflection invariant vector field

In this paper the author studies the problem of the homogenization of a diffusion perturbed by a periodic reflection invariant vector field. The vector field is assumed to have fixed direction but varying amplitude. The existence of a homogenized limit is proven and formulas for the effective diffusion constant are given. In dimension d=1 the effective diffusion constant is always less than the constant for the pure diffusion. In d>1 this property no longer holds in general.