We discuss two extensions of RPA based on a boson formalism and report on some applications within an exactly solvable many‐level pairing model. By making use of a Marumori‐type mapping procedure, we preliminary define the boson image of the fermion operators of interest and, in particular, of the model Hamiltonian. This includes two and four‐boson terms. We therefore construct renormalized RPA‐type equations in correspondence with different expansions of the boson operators. The approximate calculations are compared with the exact ones and with those obtained within RPA and Self Consistent RPA. We find that it is possible to improve considerably upon RPA by still keeping the formalism simple enough to be applied in more realistic cases without a too serious computational effort.We discuss two extensions of RPA based on a boson formalism and report on some applications within an exactly solvable many‐level pairing model. By making use of a Marumori‐type mapping procedure, we preliminary define the boson image of the fermion operators of interest and, in particular, of the model Hamiltonian. This includes two and four‐boson terms. We therefore construct renormalized RPA‐type equations in correspondence with different expansions of the boson operators. The approximate calculations are compared with the exact ones and with those obtained within RPA and Self Consistent RPA. We find that it is possible to improve considerably upon RPA by still keeping the formalism simple enough to be applied in more realistic cases without a too serious computational effort.

AIP conference proceedingsJan 1, 20050 citations

RPA ground state correlations from perturbation theory

P.J. Ellis

Nuclear Physics AOct 1, 197030 citations

Ordinary and Higher Random-Phase Approximations on the Luttinger Model

N. J. Kupelian

The exactly solvable Luttinger model for a system of one-dimensional, massless, two-component fermions interacting via general two-body forces is used as a test case for a systematically generated sequence of decoupling approximations commonly referred to as random-phase approximations (RPA) of which the simple RPA is the lowest. It is found, irrespective of both the nature and strength of the interaction, that the exact (collective) spectrum, as well as the exact correlation energy, can already be obtained in the simple RPA, and furthermore, that the next higher RPA gives a vanishing correction to these quantities. It is also shown, quite in contradistinction to the exact result, that the free-gas momentum distribution ${\overline{n}}_{k}$ persists in the second RPA as well as in the first, thereby eliminating the higher RPA as a possible approach to the calculation of ${\overline{n}}_{k}$ . Thus, in the context of this particular model, although the first few orders of RPA are highly effective for calculating the excitation spectrum and correlation energy, they are sensibly powerless in their ability to predict any variation in structure beyond that of the free-gas distribution, a result which most probably holds as well in the realistic three-dimensional case.The exactly solvable Luttinger model for a system of one-dimensional, massless, two-component fermions interacting via general two-body forces is used as a test case for a systematically generated sequence of decoupling approximations commonly referred to as random-phase approximations (RPA) of which the simple RPA is the lowest. It is found, irrespective of both the nature and strength of the interaction, that the exact (collective) spectrum, as well as the exact correlation energy, can already be obtained in the simple RPA, and furthermore, that the next higher RPA gives a vanishing correction to these quantities. It is also shown, quite in contradistinction to the exact result, that the free-gas momentum distribution ${\overline{n}}_{k}$ persists in the second RPA as well as in the first, thereby eliminating the higher RPA as a possible approach to the calculation of ${\overline{n}}_{k}$. Thus, in the context of this particular model, although the first few orders of RPA are highly effective for calculating the excitation spectrum and correlation energy, they are sensibly powerless in their ability to predict any variation in structure beyond that of the free-gas distribution, a result which most probably holds as well in the realistic three-dimensional case.

Physical ReviewApr 5, 19682 citations

Extended RPA with ground-state correlations

M. Tohyama, S. Takahara, Peter Schuck

arXiv:nucl-th/0311016The European Physical Journal AAug 1, 200411 citations

{\overline{n}}_{k}

persists in the second RPA as well as in the first, thereby eliminating the higher RPA as a possible approach to the calculation of

{\overline{n}}_{k}

. Thus, in the context of this particular model, although the first few orders of RPA are highly effective for calculating the excitation spectrum and correlation energy, they are sensibly powerless in their ability to predict any variation in structure beyond that of the free-gas distribution, a result which most probably holds as well in the realistic three-dimensional case.