Hardy inequalities for large fermionic systems

被引：0

作者：

Frank, Rupert L. ^{[1
,2
,3
]}

Hoffmann-Ostenhof, Thomas ^{[4
]}

Laptev, Ari ^{[5
,6
]}

Solovej, Jan Philip ^{[7
]}

机构：

[1] Ludwig Maximilians Univ Munchen, Math Inst, Theresienstr 39, D-80333 Munich, Germany

[2] Munich Ctr Quantum Sci & Technol, Schellingstr 4, D-80799 Munich, Germany

[3] CALTECH, Math 253-37, Pasadena, CA 91125 USA

[4] Univ Vienna, Dept Theoret Chem, Waehringerstr 17, A-1090 Vienna, Austria

[5] Imperial Coll London, 180 Queens Gate, London SW7 2AZ, England

[6] Sirius Univ Sci & Technol, Sirius Math Ctr, 1 Olymp Ave, Soci 354340, Russia

[7] Univ Copenhagen, Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen, Denmark

来源：

JOURNAL OF SPECTRAL THEORY | 2024年 / 14卷 / 02期

基金：

美国国家科学基金会;

关键词：

Hardy inequalities; fermions; semi-classical limit; electrostatic inequalities; THOMAS-FERMI; ATOMS; COLLAPSE; DENSITY;

D O I：

10.4171/JST/511

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given 0<s<(d)/(2 )with s <= 1, we are interested in the large N-behavior of the optimal constant kappa N in the Hardy inequality & sum;(N)(n=1)(-Delta(n))(s)>=kappa(N)& sum;(n<m)|X-n-X-m|(-2s), when restricted to antisymmetric functions. We show that N1-2s/d kappa(N) has a positive, finite limit given by a certain variational problem, thereby generalizing a result of Lieb and Yau related to the Chandrasekhar theory of gravitational collapse.

引用

页码：805 / 835

页数：31

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