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 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 ( 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}
}