Eigenvalue asymptotics for the one-particle kinetic energy density operator
| Autor: | Sobolev, Alexander V. |
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| Rok vydání: | 2021 |
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| Zdroj: | J. Funct. Anal. 2022 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jfa.2022.109604 |
| Popis: | 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 $\boldsymbol{\sf T}\ge 0$ with kernel $\tau(x, y)$. Comment: arXiv admin note: substantial text overlap with arXiv:2103.11896 Author's note: bounds for singular values have been considerably simplified |
| Databáze: | arXiv |
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