Sobolev, Alexander;
(2022)
Eigenvalue asymptotics for the one-particle kinetic energy density operator.
Journal of Functional Analysis
, 283
(8)
, Article 109604. 10.1016/j.jfa.2022.109604.
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Abstract
The kinetic energy of a multi-particle system is described by the one-particle kinetic energy density matrix . Alongside the one-particle density matrix it is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula, λk~(Bk)-2, B>0, as k→ ∞ , for the eigenvalues λk of the self-adjoint operator T>0 with kernel r (x, y).
| Type: | Article |
|---|---|
| Title: | Eigenvalue asymptotics for the one-particle kinetic energy density operator |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jfa.2022.109604 |
| Publisher version: | https://doi.org/10.1016/j.jfa.2022.109604 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Multi-particle Schrödinger operator, One-particle kinetic energy density matrix, Eigenvalues, Integral operators |
| UCL classification: | 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 UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10150758 |
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