Abstract In this paper we study a second-order mean-field stochastic differential systems describing the movement of particle under influence time-dependent force, friction, interaction and space noise. Using techniques from Malliavin calculus, establish explicit rates convergence in zero-mass limit (Smoluchowski-Kramers approximation) $$L^p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/Ma...

The effective independent-particle (mean-field) approximation of the Fermi–Hubbard Hamiltonian is described in a many-body basis to develop formal comparison with exact diagonalization full model using small atomic chain as test systems. This allows for development an intuitive understanding shortcomings mean-field and how critical correlation effects are missed this popular approach. descripti...