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.
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 44–54 https://doi.org/10.4213/faa3876.
To the memory of M. Z. Solomyak
Translated by A. V. Sobolev
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Sobolev, A.V. On the Spectrum of the One-Particle Density Matrix. Funct Anal Its Appl 55, 113–121 (2021). https://doi.org/10.1134/S0016266321020039
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DOI: https://doi.org/10.1134/S0016266321020039