Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation

We consider a system of N bosons interacting through a singular two-body potential scaling with N and having the form N3β −1V(Nβx) , for an arbitrary parameter β ∈ (0,1) . We provide a norm-approximation for the many-body evolution of initial data exhibiting Bose–Einstein condensation in terms of a cubic nonlinear Schrödinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations.