More precisely, after n kicks, the momentum p n of a particle with initial momentum p 0 writes p n = p 0 + K ∑ ∑ i = 0 n − − 1 sin ⁡ ⁡ θ θ i (obtained by iterating n times the standard map). Assuming that kicks are randoms and uncorrelated in time, the spreading of the momentum distribution writes ⟨ ( Δ Δ p ) 2 ⟩ = ⟨ ( p n − − p 0 ) 2 ⟩ = K 2 ∑ ∑ i = 0 n − − 1 ⟨ sin 2 θ θ i ⟩ + K 2 ∑ ∑ i ≠ ≠ j ⟨ sin ⁡ ⁡ θ θ i sin ⁡ ⁡ θ θ j ⟩ ≈ ≈ K 2 ∑ ∑ i = 0 n − − 1 ⟨ sin 2 θ θ i ⟩ = 1 2 K 2 n The classical diffusion coefficient in momentum direction is then given in first approximation by D cl = K 2 4 . Corrections coming from neglected correlation terms can actually be taken into account, leading to the improved expression D cl = K 2 4 [ 1 − − 2 J 2 ( K ) + 2 J 2 2 ( K ) ] where J 2 is the Bessel function of first kind.