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.
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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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