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Special Topics

EPJB Colloquium - Fulfillment of sum-rules and Goldstone modes in many body theories

Schematic representation of the two body mean field

This EPJ B Colloquium article explores applications of the Self-Consistent Random Phase Approximation (SCRPA) approach to Fermi systems with a continuously broken symmetry. Correlations beyond those considered by standard Random Phase Approximation (RPA) are summed up, thereby correcting for the quasi-boson approximation in standard RPA.

Desirable properties of standard RPA, such as fulfilment of the energy-weighted sum rule and the appearance of Goldstone (zero) modes, are preserved. The authors show theoretically as well as numerically, for a model case, that SCRPA maintains all the properties of standard RPA for practically all instances of spontaneously-broken symmetries. A simpler approximate form of SCRPA, the so-called renormalised RPA, also exhibits these properties. The SCRPA equations are first outlined as an eigenvalue problem, and then it is shown how an equivalent many-body Green’s function approach can be formulated.

Managing Editors
Anne Ruimy and Vijala Kiruvanayagam (EDP Sciences) and Sabine Lehr (Springer-Verlag)
Dear Sabine and Isabelle,
Thank you so much for all your help and excellent work you did on the EPJ ST volume "Nonlinear Dynamics of Deterministic and Stochastic Systems: Unraveling Complexity". This was a great experience and collaboration.

Alexander Neiman (on behalf of the guest editors), Ohio University, Athens, USA
Editor EPJ Special Topics 222/10, 2013

ISSN: 1951-6355 (Print Edition)
ISSN: 1951-6401 (Electronic Edition)

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