Monte Carlo simulations of the randomly forced Burgers equation

The behaviour of the one-dimensional random-forced Burgers equation is investigated in the path integral formalism, using a discrete space-time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as structure functions, as ensemble averages over different field realizations. The regularization of shock solutions to the zero-viscosity limit (Hopf equation) eventually leads to constraints on lattice parameters, required for the stability of the simulations. Insight into the formation of localized structures (shocks) and their dynamics is obtained.