On the Spectrum of the One-Particle Density Matrix

• Published in: Functional analysis and its applications Vol. 55; no. 2; pp. 113 - 121
• Main Author: Sobolev, A. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-04-2021; Springer Nature B.V
• Subjects: 14/34; 639/766/189; 639/766/530; 639/766/747; Analysis; Eigenvalues; Functional Analysis; Mathematics; Mathematics and Statistics; Operators (mathematics); Particle density (concentration); eigenvalues; multi-particle Schrödinger operator; one-particle density matrix; asymptotics; integral operators
• ISSN: 0016-2663; 1573-8485
• DOI: 10.1134/S0016266321020039

The one-particle density matrix
is one of the key objects in quantum-mechanical approximation schemes. The self-adjoint operator
with kernel
is trace class, but no sharp results on the decay of its eigenvalues were previously known. The note presents the asymptotic formula
,
, as
for the eigenvalues
of the operator
and describes the main ideas of the proof.