Year: 2025
Type: preprint
Abstract: We prove that the eigenvalues of a 2-body operator $γ_{2}^Ψ$ associated to a fermionic $N$-particle state $Ψ$ are highly constrained by the structure of the corresponding eigenvectors: If $Φ=\sum_{k=1}^{\infty}λ_{k}u_{k}\wedge v_{k}$ is the canonical form of an eigenvector $Φ$ with eigenvalue $Λ$, then $Λ\leq(1+\frac{N-2}{2}\sum_{k=1}^{\infty}λ_{k}^{4})^{-1}N$. We also prove a lower bound on $\sup_{\Vert Ψ\Vert =1}\langle Φ,γ_{2}^ΨΦ\rangle$ for fixed $Φ$, and state a conjecture motivated by these results.
Source: arXiv (Cornell University)
Author: Christiansen, Martin Ravn
Institution: Institute of Science and Technology Austria
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415036963
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