Eigenvalue asymptotics for the one-particle kinetic energy density operator

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

No reviews yet.

No comments yet.