Trajectory simulation of kinetic equations for classical systems

We formulate a linear theory of physical kinetics describing the relaxation of atoms from a non-equilibrium distribution. The evolution of the single-particle distribution function is decomposed into trajectories, each corresponding to a different realization of a sequence of collisions. Accumulating all possible trajectories gives the dynamics described by the classical Boltzmann equation. The significance of our method is that the required computation time scales linearly with the number of points used to sample the distribution function. This leads to the interesting possibility of extending our method to consider quantum coherences and the growth of long-range order in Bose - Einstein condensation where a large set of basis states may be required.