Eigenvalue asymptotics for the one-particle density matrix

2021/03/22 by Alexander V. Sobolev, Sobolev, Alexander V. · 1 citation
Chemistry · Computer Science · Mathematics · #81Q10 #Advanced Physical and Chemical Molecular Interactions #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Primary 35J10 #Secondary 47G10 #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2103.11896

openalex publication_date 2021/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The one-particle density matrix γ(x, y) for a bound state of an atom or molecule is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula λ_k ∼ (Ak)^-8/3, A ≥ 0, as k→∞, for the eigenvalues λ_k of the self-adjoint operator \boldsymbolΓ≥ 0 with kernel γ(x, y).

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• Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix

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