2014/07/30 by P. Papakonstantinou · 26 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Computer science #Mathematical Approximation and Integration #Mathematical functions and polynomials #Mathematical physics #Mathematics #Scientific Research and Discoveries #Stability (learning theory) #cond-mat.other #cond-mat.str-el #nucl-th
paper · pdf · doi:10.1103/physrevc.90.024305
published in Physical Review C 90(2) (American Institute of Physics) · 11 pages, incl. 5 figures; to appear in Phys. Rev. C
arxiv created 2014/07/30 · openalex publication_date 2014/08/11 · arxiv updated 2014/09/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
It has been revealed through numerical calculations that the second random phase approximation (SRPA) with the Hartree-Fock solution as its reference state results in 1. spurious states at genuinely finite energy, contrary to common expectation, and 2. unstable solutions, which within the first-order random phase approximation correspond to real low-energy collective vibrations. In the present work, these shortcomings of SRPA are shown to not contradict Thouless' theorem about the energy-weighted sum rule, and their origin is traced to the violation of the stability condition. A more general theorem is proven. Formal arguments are elucidated through numerical examples. Implications for the validity of the SRPA are discussed.