Abstract Several hydrodynamic models of the atomic Bose–Einstein condensate (BEC) obtained beyond mean-field approximation are discussed together from a single point view. All these derived microscopic quantum description. The derivation is made within many-particle hydrodynamics method suggested by L Kuz’menkov. demonstrated and for regime revealing Gross–Pitaevskii equation as simplest illust...

We propose an approximation framework that unifies and generalizes a number of existing mean-field approximation methods for the susceptible-infected-susceptible (SIS) epidemic model on complex networks. We derive the framework, which we call the unified mean-field framework (UMFF), as a set of approximations of the exact Markovian SIS equations. Our main novelty is that we describe the mean-fi...

Starting from full quantum field theory, various mean field approaches are derived systematically. With a full consideration of external source dependence , the stationary phase approximation of an action gives a nuclear mean field theory which includes quantum correlation effects (such as particle-hole or ladder diagram) in a simpler way than the Brueckner-Hartree-Fock approach. Implementing f...