Eigenvalue Bounds for Multi-Particle Reduced Density Matrices of Coulombic Wavefunctions

2024/12/20 by Hearnshaw, Peter · 1 citation
#35J10 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2412.16073

Abstract

For bound states of atoms and molecules of N electrons we consider the corresponding K-particle reduced density matrices, Γ^(K), for 1 ≤ K ≤ N-1. Previously, eigenvalue bounds were obtained in the case of K=1 and K=N-1 by A.V. Sobolev. The purpose of the current work is to obtain bounds in the case of 2 ≤ K ≤ N-2. For such K we label the eigenvalues of the positive, trace class operators Γ^(K) by λ_n(Γ^(K)) for n=1,2,…, and obtain the bounds λ_n(Γ^(K)) ≤ Cn^-α_K for all n, where α_K = 1 + 7/(3L) and L = min\K,N-K\.

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

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