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This paper investigates the algebraic geometry of eigenvector varieties within linear spaces, specifically targeting their application to Lie algebras and quantum Hamiltonians. By systematically studying these mathematical structures, the work advances theoretical frameworks essential for understanding spectral properties in complex quantum systems.

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Eigenvector Varieties

arXiv19 august 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2606.20432v2 Announce Type: replace-cross Abstract: Any linear space of square matrices has an associated eigenvector variety. Its points are eigenvectors of matrices from that linear space. We present a systematic study of eigenvector varieties, with focus on Lie algebras and Hamiltonians of quantum systems.

Abstract:Any linear space of square matrices has an associated eigenvector variety. Its points are eigenvectors of matrices from that linear space. We present a systematic study of eigenvector varieties, with focus on Lie algebras and Hamiltonians of quantum systems.

Algebraic Geometry (math.AG); Rings and Algebras (math.RA); Quantum Physics (quant-ph)

arXiv:2606.20432 [math.AG]

(or arXiv:2606.20432v2 [math.AG] for this version)

https://doi.org/10.48550/arXiv.2606.20432 Focus to learn more arXiv-issued DOI via DataCite

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