Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker Functionals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929724750561280 |
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| author | Benguria, Rafael D. Siedentop, Heinz |
| author_facet | Benguria, Rafael D. Siedentop, Heinz |
| contents | We bound the number of electrons $Q$ that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizsäcker functional: instead of the classical power $5/3$ more general powers $p$ are considered. For $3/2<p<2$ we prove the excess charge conjecture, i.e., that $Q$ is uniformly bounded in the atomic number $Z$. The case $p=3/2$ is critical: the behavior changes from a uniform bound in $Z$ to a linear bound at the critical coupling $4\sqrtπ$ of the nonlinear term. We also improve the linear bound for all $p\geq6/5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker Functionals Benguria, Rafael D. Siedentop, Heinz Mathematical Physics Analysis of PDEs 81V45, 81V55, 35Q40 We bound the number of electrons $Q$ that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizsäcker functional: instead of the classical power $5/3$ more general powers $p$ are considered. For $3/2<p<2$ we prove the excess charge conjecture, i.e., that $Q$ is uniformly bounded in the atomic number $Z$. The case $p=3/2$ is critical: the behavior changes from a uniform bound in $Z$ to a linear bound at the critical coupling $4\sqrtπ$ of the nonlinear term. We also improve the linear bound for all $p\geq6/5$. |
| title | Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker Functionals |
| topic | Mathematical Physics Analysis of PDEs 81V45, 81V55, 35Q40 |
| url | https://arxiv.org/abs/2502.15444 |