Time Scales in Homogenization of Periodic Flows with Vanishing Molecular Diffusion

We study the long time transport property of conservative systems perturbed by a small white noise. We introduce the dissipation and martingale times and show how they are related to the diffusion time on which a limit theorem is valid. The limit theorem is a probabilistic version of homogenization with vanishing molecular diffusion. Examples of nontrivial time scales are given.