Physical and unphysical solutions of random-phase approximation equation

H. Nakada

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arXiv · 1604.07972

Physical and unphysical solutions of random-phase approximation equation

H. Nakada

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Abstract

Properties of solutions of the RPA equation is reanalyzed mathematically, which is defined as a generalized eigenvalue problem of the stability matrix $\mathsf{S}$ with the norm matrix $\mathsf{N}=\mathrm{diag.}(1,-1)$. As well as physical solutions, unphysical solutions are examined in detail, with taking the possibility of Jordan blocks of the matrix $\mathsf{N\,S}$ into consideration. Two types of duality of eigenvectors and basis vectors of the Jordan blocks are pointed out and explored, which disclose many basic properties of the RPA solutions.

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H. Nakada. 2016-04-27. Physical and unphysical solutions of random-phase approximation equation. https://arxiv.org/abs/1604.07972

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