Recall that the diffusion coefficient is D c l ≈ ≈ K 2 / 2 , because the change ( p ( t ) − − p ( 0 ) ) in the momentum is the sum of quasi-random kicks K sin ⁡ ⁡ ( x ( n ) ) . An exact expression for D c l is obtained by calculating the "area" of the correlation function C ( n ) = ⟨ ⟨ sin ⁡ ⁡ ( x ( n ) ) sin ⁡ ⁡ ( x ( 0 ) ) ⟩ ⟩ , namely the sum D = K 2 ∑ ∑ C ( n ) . Note that C ( 0 ) = 1 / 2 . The same calculation recipe holds also in the quantum mechanical case, and also if noise is added.