Eigenvalue asymptotics for the one-particle kinetic energy density operator

Abstract

The kinetic energy of a multi-particle system is described by the one-particle kinetic energy density matrix $\tau (x,y)$. Alongside the one-particle density matrix $\gamma (x,y)$, it is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula ${\lambda }_k\sim (Bk{)}^{-2}$, $B\ge 0$, as $k\to \infty$, for the eigenvalues ${\lambda }_k$ of the self-adjoint operator $\mathsf{T}\ge 0$ with kernel $\tau (x,y)$.

arXiv admin note: substantial text overlap with arXiv:2103.11896 Author's note: bounds for singular values have been considerably simplified

References in corpus (1)

• Geometric methods for nonlinear many-body quantum systems

Cited by in corpus (3)

• The Scott conjecture for large Coulomb systems: a review
• The diagonal behaviour of the one-particle Coulombic density matrix
• Regularity of the (N-1)-particle electronic reduced density matrix for molecules with fixed nuclei and N electrons