The effective potential in scalar quantum field theory is calculated using different expansions of the path integral for the generating functional. The conventional loop expansion is compared with the interpolated, optimized, and mean-field expansions in the lowest orders. The optimized expansion is studied up to third order. In the space-time dimensions 0 and 1 the comparison with the "exact" effective potential calculated numerically shows that the only method which gives qualitative agreement in the whole range of Lagrangian parameters is the mean-field expansion. In 4 dimensions the mean-field method seems also to be most reliable and the theory to be noninteracting. 1835

Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic approximation appears exact in the strong interaction limit, allowing determination of the asymptotic expression for the linear entropy. Entanglement properties are dramatically influenced by the anisotropy of the confining potential in the strong-correlation regime.

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We investigate quantum correlations in the ground state of the Moshinsky model formed by N harmonically interacting particles confined in a harmonic potential. The model is solvable which allows an exact determination of entanglement between the subset of p particles and the remaining N − p particles. We study linear entropies and von Neumann entropies of the bipartitions and compare their behavior with that of the relative correlation energy and of the statistical Kutzelnigg coefficient.

We examine the entanglement in the ground states of helium and helium-like ions using an original Hylleraas expansion. The von Neumann and linear entropies of the reduced density matrix are accurately computed by performing the Schmidt decomposition of the S singlet spatial wavefunctions. The results presented are more accurate than currently available in published literature.