Coefficients of almost-degenerate density matrix perturbation theory for eigenvalue problems
Mathematical Physics
2023-07-11 v2 math.MP
Quantum Physics
Abstract
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become singular because inverses of differences between eigenvalues arise as some factors. We remove those artificial singularities in the expressions of the coefficients of the series, allowing eigenvalue gaps to be arbitrarily small and even vanishing in the resulting formulas.
Cite
@article{arxiv.2305.09026,
title = {Coefficients of almost-degenerate density matrix perturbation theory for eigenvalue problems},
author = {Charles Arnal and Louis Garrigue},
journal= {arXiv preprint arXiv:2305.09026},
year = {2023}
}
Comments
The result already exists in another article and we did not know. We will reuse the same methods (that where developed in the withdrawn article) in a forthcoming document, but this will have a different title and a different abstract