Geodesic
On the spectrum of the one-particle density matrix
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 2, pp. 44-54.

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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. 
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A. V. Sobolev. On the spectrum of the one-particle density matrix. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 2, pp. 44-54. http://geodesic.mathdoc.fr/item/FAA_2021_55_2_a3/

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