THE SEMICLASSICAL LIMIT OF THE TIME DEPENDENT HARTREE-FOCK EQUATION: THE WEYL SYMBOL OF THE SOLUTION

被引：22

作者：

Amour, Laurent ^{[1
]}

Khodja, Mohamed ^{[1
]}

Nourrigat, Jean ^{[1
]}

机构：

[1] Univ Reims, Lab Math Reims, FR CNRS 3399, EA 4535, F-51687 Reims, France

来源：

ANALYSIS & PDE | 2013年 / 6卷 / 07期

关键词：

time dependent Hartree-Fock equation; Vlasov equation; semiclassical analysis; Egorov theorem; pseudodifferential operators; MEAN-FIELD LIMIT; DYNAMICS; SYSTEMS;

D O I：

10.2140/apde.2013.6.1649

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a family of solutions to the time dependent Hartree-Fock equation, depending on the semiclassical parameter h, we prove that if at the initial time the Weyl symbol of the solution is in L-1(R-2n) as well as all its derivatives, then this property is true for all time, and we give an asymptotic expansion in powers of h of this Weyl symbol. The main term of the asymptotic expansion is a solution to the Vlasov equation, and the error term is estimated in the norm of L-1(R-2n).

引用

页码：1649 / 1674

页数：26

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