Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914808595480576 |
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| author | Kitahama, Shunta Yoshida, Hironobu Toyota, Ryo Katsura, Hosho |
| author_facet | Kitahama, Shunta Yoshida, Hironobu Toyota, Ryo Katsura, Hosho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01166 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms Kitahama, Shunta Yoshida, Hironobu Toyota, Ryo Katsura, Hosho Quantum Physics Statistical Mechanics Mathematical Physics 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. |
| title | Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2308.01166 |