Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms
Quantum Physics
2024-05-27 v3 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We give a rigorous proof of Conjecture 3.1 by Prosen [Prosen T 2010 J. Stat. Mech. P07020] on the nilpotent part of the Jordan decomposition of a quadratic fermionic Liouvillian. We also show that the number of the Jordan blocks of each size can be expressed in terms of the coefficients of a polynomial called the -binomial coefficient and describe the procedure to obtain the Jordan canonical form of the nilpotent part.
Cite
@article{arxiv.2308.01166,
title = {Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms},
author = {Shunta Kitahama and Hironobu Yoshida and Ryo Toyota and Hosho Katsura},
journal= {arXiv preprint arXiv:2308.01166},
year = {2024}
}
Comments
12 pages, no figures; v3: some remarks added