Direct Simulation Monte Carlo method for cold atom dynamics: classical Boltzmann equation in the quantum collision regime

In this paper we develop a direct simulation Monte Carlo (DSMC) method for simulating highly nonequilibrium dynamics of nearly degenerate ultra-cold gases. We show that our method can simulate the high-energy collision of two thermal clouds in the regime observed in experiments [Thomas, et al. Phys. Rev. Lett. \textbf{93}, 173201 (2004)], which requires the inclusion of beyond s-wave scattering. We also consider the long-time dynamics of this system, demonstrating that this would be a practical experimental scenario for testing the Boltzmann equation and studying rethermalization.