Quantum diffusion of the random Schrodinger evolution in the scaling limit II. The recollision diagrams

We consider random Schrodinger equations on R-d for d = 3 with a homogeneous Anderson-Poisson type random potential. Denote by. the coupling constant and psi(t) the solution with initial data psi(0). The space and time variables scale as lambda(-2-kappa/2), t similar to lambda(-2-kappa) with 0 < kappa < kappa(0)(d). We prove that, in the limit lambda -> 0, the expectation of the Wigner distribution of psi(t) converges weakly to the solution of a heat equation in the space variable x for arbitrary L-2 initial data. The proof is based on a rigorous analysis of Feynman diagrams. In the companion paper [ 10] the analysis of the non-repetition diagrams was presented. In this paper we complete the proof by estimating the recollision diagrams and showing that the main terms, i. e. the ladder diagrams with renormalized propagator, converge to the heat equation.