数苑经纬讲坛（129）：Eigenvalue asymptotics of Müller minimizers for atoms
来源：
发布时间：2026-11-12
报告时间：- German Time: 9:00--, November 12 (Thursday), 2026;Beijing Time: 16:00--, November 12 (Thursday), 2026;
- 报告地点：
- Zoom code: 983 309 9626 Password: 202611
- 报告人：
- Professor Rupert L. Frank, LMU Munich
- 报告人单位：
- Germany
- 邀请人：
- 郭玉劲
- 摘要：
- We study the spectral properties of minimizers of the Müller functional for atoms with Nelectrons and nuclear charge Z. We prove that under some suitable assumptions on Zand N, the k-th eigenvalue of a Müller minimizer γ∗behaves as A∗k−8/3when k→∞, with a constant A∗>0determined explicitly by the density of γ∗. In particular, our assumption holds if Zis sufficiently large and N≤Z−C0Z1/3. While our proof is inspired by Sobolev's work on the asymptotic behavior of the one-particle density matrix of Schrödinger ground states, the analysis in Müller theory requires several new ingredients concerning both the singular behavior of the integral kernel of the minimizers near the diagonal and the decay properties at infinity. The talk is based on joint work with L. Meng, P. T. Nam and H. Siedentop.
Professor Rupert L. Frank, LMU Munich (Germany)
