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
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.
© SIF, Springer-Verlag Berlin Heidelberg, 2016