⟨ η η i ( t ) η η j ( t ′ ) ⟩ = 2 λ λ k B T δ δ i , j δ δ ( t − − t ′ ) , where k B is Boltzmann's constant, T is the temperature and η η i ( t ) is the i-th component of the vector η η ( t ) . The δ δ -function form of the time correlation means that the force at a time t is 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 δ δ -correlation and the Langevin equation becomes virtually exact.