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arXiv · 2308.01166

Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms

Shunta Kitahama·Hironobu Yoshida·Ryo Toyota·Hosho Katsura
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Abstract

We give a rigorous proof of Conjecture 3.1 by Prosen [Prosen T 2010 J. Stat. Mech. $\textbf{2010}$ 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 $q$-binomial coefficient and describe the procedure to obtain the Jordan canonical form of the nilpotent part.

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Shunta Kitahama, Hironobu Yoshida, Ryo Toyota, Hosho Katsura. 2023-08-02. Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms. https://doi.org/10.1088/1742-5468%2Fad0f98

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