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We consider the final-data problem for systems of nonlinear Schr\"odingerequations with $L^2$ subcritical nonlinearity. An asymptotically free solutionis uniquely obtained for almost every randomized asymptotic profile in$L^2(\mathbb{R}^d)$, extending the result of J. Murphy to powers equal to orlower than the Strauss exponent. In particular, systems with quadraticnonlinearity can be treated in three space dimensions, and by the sameargument, the Gross-Pitaevskii equation in the energy space. The extension isby use of the Strichartz estimate with a time weight.

Randomized final-data problem for Systems of Nonlinear Schr\"odinger Equations and the Gross-Pitaevskii Equation