Eigenvalue asymptotics for the one-particle kinetic energy density operator

摘要

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 similar to (Bk)-2, B 0, as k -> infinity, for the eigenvalues lambda k of the self-adjoint operator T 0 with kernel Tau(x, y).(c) 2022 The Author. Published by Elsevier Inc.