Time evolution of correlation functions and thermalization 
I presented a numerical study of the time evolution of a classical ensemble of isolated periodic chains of O(N)-symmetric anharmonic oscillators. The method is based on an exact evolution equation for the time dependence of correlation functions , in an approximation which retains all contributions in next-to-leading order in a 1/N expansion and preserves time reflection symmetry. The evolution displays effective irreversibility and approximate thermalization but generically the system approaches - at large times -stationary solutions that are not consistent with thermal equilibrium. The ensemble therefore seems to retain some memory of the initial condition beyond the conserved total energy. Such a behavior with incomplete thermalization is expected for systems in a small volume. Surprisingly, it was found that - within our truncation scheme and numerical approximations - the nonthermal asymptotic stationary solutions do not change for large volume, which raises questions on the existence and dynamical role of nonthermal stable fixed points in the evolution and, more generally, on Boltzmann's conjecture that macroscopic isolated systems thermalize.
Talk based on: hep-ph/9907533
 C. Wetterich, hep-th/9612206, hep-th/9703006.