where formula_7 is Boltzmann's constant, formula_8 is the temperature and formula_9 is the i-th component of the vector formula_4. The formula_11-function form of the correlations in time means that the force at a time formula_12 is assumed to be completely uncorrelated with the force at any other time. This is an approximation; the actual random force has a nonzero correlation time corresponding to the collision time of the molecules. However, the Langevin equation is used to describe the motion of a "macroscopic" particle at a much longer time scale, and in this limit the formula_11-correlation and the Langevin equation becomes virtually exact.