Eur. Phys. J. A (2016) 52: 307
https://doi.org/10.1140/epja/i2016-16307-7

Review

Self-consistent RPA and the time-dependent density matrix approach

¹ Institut de Physique Nucléaire, F-91406, Orsay CEDEX, France
² Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS and Université Joseph Fourier, 25 Avenue des Martyrs BP166, F-38042, Grenoble Cédex 9, France
³ Kyorin University School of Medicine, 181-8611, Mitaka, Tokyo, Japan

^* e-mail: schuck@ipno.in2p3.fr

Received: 4 May 2016
Accepted: 29 August 2016
Published online: 11 October 2016

Abstract

The time-dependent density matrix (TDDM) or BBGKY (Bogoliubov, Born, Green, Kirkwood, Yvon) approach is decoupled and closed at the three-body level in finding a natural representation of the latter in terms of a quadratic form of two-body correlation functions. In the small amplitude limit an extended RPA coupled to an also extended second RPA is obtained. Since including two-body correlations means that the ground state cannot be a Hartree-Fock state, naturally the corresponding RPA is upgraded to Self-Consistent RPA (SCRPA) which was introduced independently earlier and which is built on a correlated ground state. SCRPA conserves all the properties of standard RPA. Applications to the exactly solvable Lipkin and the 1D Hubbard models show good performances of SCRPA and TDDM.