Mean Field Derivation of DNLS from the Bose–Hubbard Model

Abstract We prove that the flow of discrete nonlinear Schrödinger equation (DNLS) is mean field limit quantum dynamics Bose–Hubbard model for N interacting particles. In particular, we show Wick symbol annihilation operators evolved in Heisenberg picture converges, as becomes large, to solution DNLS. A quantitative $$L^p$$ L p -estimate, any $$p \ge 1$$ ≥ 1 , obtained with a linear dependence on time due Gaussian measure initial data coherent states.