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On the Spectrum of the One-Particle Density Matrix
Functional Analysis and Its Applications ( IF 0.4 ) Pub Date : 2021-11-08 , DOI: 10.1134/s0016266321020039
A. V. Sobolev 1
Affiliation  

Abstract

The one-particle density matrix \(\gamma(x, y)\) is one of the key objects in quantum-mechanical approximation schemes. The self-adjoint operator \(\Gamma\) with kernel \(\gamma(x, y)\) is trace class, but no sharp results on the decay of its eigenvalues were previously known. The note presents the asymptotic formula \(\lambda_k \sim (Ak)^{-8/3}\), \(A \ge 0\), as \(k\to\infty\) for the eigenvalues \(\lambda_k\) of the operator \(\Gamma\) and describes the main ideas of the proof.



中文翻译:

关于单粒子密度矩阵的谱

摘要

单粒子密度矩阵\(\gamma(x, y)\)是量子力学近似方案中的关键对象之一。具有核\(\gamma(x, y)\)的自伴随算子\(\Gamma\)是迹类,但之前没有关于其特征值衰减的明显结果是已知的。笔记提出了渐近公式\(\lambda_k \sim (Ak)^{-8/3}\) , \(A \ge 0\),如\(k\to\infty\)的特征值\(\ lambda_k\)的运算符\(\Gamma\)并描述了证明的主要思想。

更新日期:2021-11-09
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