BROWNIAN DYNAMICS SIMULATIONS WITHOUT GAUSSIAN RANDOM NUMBERS

Abstract

We point out that in a Brownian dynamics simulation it is justified to use arbitrary distribution functions of random numbers if the moments exhibit the correct limiting behavior prescribed by the Fokker-Planck equation. Our argument is supported by a simple analytical consideration and some numerical examples: We simulate the Wiener process, the Ornstein-Uhlenbeck process and the diffusion in a Φ 4 potential, using both Gaussian and uniform random numbers. In these examples, the rate of convergence of the mean first exit time is found to be nearly identical for both types of random numbers.