Time evolution of correlation functions for classical and quantum   anharmonic oscillators
  The time evolution of the correlation functions of an ensemble of anharmonic N-component oscillators with O(N) symmetry is described by a flow equation, exact up to corrections of order $1/N^2$. We find effective irreversibility. Nevertheless, analytical and numerical investigation reveals that the system does not reach thermal equilibrium for large times, even when $N\to \infty$. Depending on the initial distribution, the dynamics is asymptotically stable or it exhibits growing modes which break the conditions for the validity of the 1/N expansion for large time. We investigate both classical and quantum systems, the latter being the limit of an O(N) symmetric scalar quantum field theory in zero spatial dimensions. 
Luis M.A. Bettencourt (Los Alamos) and C. Wetterich (U. of Heidelberg)