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On the Spectrum of the One-Particle Density Matrix

Sobolev, A; (2021) On the Spectrum of the One-Particle Density Matrix. Functional Analysis and Its Applications , 55 (2) pp. 113-121. 10.1134/S0016266321020039. Green open access

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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.

Type: Article
Title: On the Spectrum of the One-Particle Density Matrix
Open access status: An open access version is available from UCL Discovery
DOI: 10.1134/S0016266321020039
Publisher version: https://doi.org/10.1134/S0016266321020039
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
Keywords: multi-particle Schrodinger operator, one-particle density matrix, eigenvalues, asymptotics, integral operators
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10139605
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