Mean field dynamics of fermions and the time-dependent Hartree-Fock equation

被引:80
作者
Bardos, C
Golse, F
Gottlieb, AD
Mauser, NJ
机构
[1] Univ Paris 07, F-75252 Paris 05, France
[2] Lab Jacques Louis Lions, F-75252 Paris 05, France
[3] Univ Vienna, Wolfgang Pauli Inst, Inst Math, A-1090 Vienna, Austria
来源
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2003年 / 82卷 / 06期
关键词
Hartree-Fock equations; quantum N-body problem; mean-field limit;
D O I
10.1016/S0021-7824(03)00023-0
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The time-dependent Hartree-Fock equations are derived from the N-body linear Schrodinger equation with the mean-field scaling in the limit N --> +infinity and for initial data that are close to Slater determinants. Only the case of bounded, symmetric binary interaction potentials is treated in this work. We prove that, as N --> +infinity, the first partial trace of the N-body density operator approaches the solution of the time-dependent Hartree-Fock equations (in operator form) in the sense of the trace norm. (C) 2003 Editions scientifiques et medicales Elsevier SAS. All rights reserved.
引用
收藏
页码:665 / 683
页数:19
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