Brownian motion of interacting and noninteracting particles subject to a periodic potential and driven by an external field

We discuss the mean-velocity field characteristic associated with the Brownian motion of interacting and noninteracting particles subject to a periodic potential and driven by an external field. This is carried out by means of the Smoluchowski equation and its first correction and by means of a molecular-dynamics technique. Moreover, we explore the phase-transition-threshold analogy and demonstrate that the critical exponents are not affected by the first correction term and the interaction.