Global well-posedness and scattering for energy-critical Schrodinger equations with conservative Marcus noise

Abstract

This work establishes global well-posedness for the three-dimensional defocusing energy-critical nonlinear Schr\"odinger equation with conservative linear Marcus noise. For arbitrary deterministic energy-space data, we construct a probabilistically strong solution, unique in the critical spacetime class, and prove convergence of finite-activity approximations. The spatial profiles need only be bounded and Lipschitz, while the centered pure-jump L\'evy noise is assumed to have finite second moment. If the temporal noise coefficient is square integrable on the half-line, the solution scatters almost surely, with uniform mean-square tail convergence and no smallness restriction. The solution conserves mass and satisfies an exact energy balance. The proof combines deterministic energy-critical stability with Poisson Strichartz estimates; convergence of the interaction-representation martingale gives the critical spacetime control needed for continuation and scattering.