  We present a novel approach to investigate the long-time stochastic dynamics
of multi-dimensional classical systems, in contact with a heat-bath. When the
potential energy landscape is rugged, the kinetics displays a decoupling of
short and long time scales and both
  Molecular Dynamics (MD) or Monte Carlo (MC) simulations are generally
inefficient. Using a field theoretic approach, we perform analytically the
average over the short-time stochastic fluctuations. This way, we obtain an
effective theory, which generates the same long-time dynamics of the original
theory, but has a lower time resolution power. Such an approach is used to
develop an improved version of the MC algorithm, which is particularly suitable
to investigate the dynamics of rare conformational transitions. In the specific
case of molecular systems at room temperature, we show that elementary
integration time steps used to simulate the effective theory can be chosen a
factor ~100 larger than those used in the original theory. Our results are
illustrated and tested on a simple system, characterized by a rugged energy
landscape.
