Abstract:
The one-particle density matrix $\gamma(x, y)$
is one of the key objects in quantum-mechanical approximation schemes.
The self-adjoint
operator $\Gamma$ with kernel $\gamma(x, y)$ is trace class, but no sharp results on the decay of
its eigenvalues
were previously known. The note presents the asymptotic formula $\lambda_k \sim (Ak)^{-8/3}$, $A \ge 0$,
as $k\to\infty$
for the eigenvalues $\lambda_k$ of the operator $\Gamma$ and describes the main ideas of the proof.
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