English

Solutions of random-phase approximation equation for positive-semidefinite stability matrix

Nuclear Theory 2016-06-13 v1

Abstract

It is mathematically proven that, if the stability matrix S\mathsf{S} is positive-semidefinite, solutions of the random-phase approximation (RPA) equation are all physical or belong to Nambu-Goldstone (NG) modes, and the NG-mode solutions may form Jordan blocks of NS\mathsf{N\,S} (N\mathsf{N} is the norm matrix) but their dimension is not more than two. This guarantees that the NG modes in the RPA can be separated out via canonically conjugate variables.

Cite

@article{arxiv.1606.03167,
  title  = {Solutions of random-phase approximation equation for positive-semidefinite stability matrix},
  author = {H. Nakada},
  journal= {arXiv preprint arXiv:1606.03167},
  year   = {2016}
}
R2 v1 2026-06-22T14:22:12.836Z