Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms

Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms

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 coeffic...

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Veröffentlicht in:arXiv.org 2023-11
Hauptverfasser: Kitahama, Shunta, Yoshida, Hironobu, Toyota, Ryo, Katsura, Hosho
Format: Artikel
Sprache:eng
Schlagworte:
Canonical forms
Decomposition
Polynomials
Quadratic forms
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Zusammenfassung: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.
ISSN:2331-8422