An application of the Bohm-Pines equation to a system of interacting bosons

節夫 三沢

Gert Roepstorff

Niels Benedikter

Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation.

K. K. Singh

節夫 三沢

Hugenholtz and Pines have developed a new method evaluate the ground state energy of a system of interacting bosons, the merit of which consists in the elimination of ' the zero-momentam state and accordingly the applicability of the linked cluster expansion. Their theory, however, does not give correct results because of the undue treatment of the zero-momentum state; this is proved in a simple example. Up to the third order coupling parameter of the ground state enengy, the result of the usual RayleighSchrodinger perturbation method are compared with that obtained according to Hugenholtz-Pines' theory. The latter does not agree with the former. (auth)

Phan Thành Nam

We review the bosonization method for Fermi gases, initiated by Sawada, Bohm–Pines, and Gell-Mann–Brueckner in the 1950s, and present recent rigorous results that justify this approach in the mean-field regime with regular and Coulomb interactions, as well as in the low-density regime leading to the Huang–Yang formula. We also discuss some open questions on related topics.