Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches

TL;DR

This paper reviews and compares various extensions of the Random Phase Approximation (RPA) for strongly correlated Fermi systems, emphasizing the Equation of Motion Method and Green's function approach, with applications to nuclear matter and model systems.

Contribution

It provides a comprehensive framework for extended RPA methods, including SCRPA, r-RPA, and ESRPA, analyzing their treatment of Pauli correlations and thermodynamic properties.

Findings

Comparison of different RPA extensions and their treatment of Pauli correlations.

Application of extended RPA methods to nuclear matter and model systems.

Discussion of cluster approximations and particle RPA approaches.

Abstract

The status of different extensions of the Random Phase Approximation (RPA) is reviewed. The general framework is given within the Equation of Motion Method and the equivalent Green's function approach for the so-called Self-Consistent RPA (SCRPA). The role of the Pauli principle is analyzed. A comparison among various approaches to include Pauli correlations, in particular, renormalized RPA (r-RPA), is performed. The thermodynamic properties of nuclear matter are studied with several cluster approximations for the self-energy of the single-particle Dyson equation. More particle RPA's are shortly discussed with a particular attention to the alpha-particle condensate. Results obtained concerning the Three-level Lipkin, Hubbard and Picket Fence Models, respectively, are outlined. Extended second RPA (ESRPA) is presented.